diff --git a/core/src/main/java/org/elasticsearch/common/util/set/Sets.java b/core/src/main/java/org/elasticsearch/common/util/set/Sets.java
index f2bba5cde36..0f1fe22c020 100644
--- a/core/src/main/java/org/elasticsearch/common/util/set/Sets.java
+++ b/core/src/main/java/org/elasticsearch/common/util/set/Sets.java
@@ -71,12 +71,31 @@ public final class Sets {
         return !left.stream().anyMatch(k -> right.contains(k));
     }
 
+    /**
+     * The relative complement, or difference, of the specified left and right set. Namely, the resulting set contains all the elements that
+     * are in the left set but not in the right set. Neither input is mutated by this operation, an entirely new set is returned.
+     *
+     * @param left  the left set
+     * @param right the right set
+     * @param <T>   the type of the elements of the sets
+     * @return the relative complement of the left set with respect to the right set
+     */
     public static <T> Set<T> difference(Set<T> left, Set<T> right) {
         Objects.requireNonNull(left);
         Objects.requireNonNull(right);
         return left.stream().filter(k -> !right.contains(k)).collect(Collectors.toSet());
     }
 
+    /**
+     * The relative complement, or difference, of the specified left and right set, returned as a sorted set. Namely, the resulting set
+     * contains all the elements that are in the left set but not in the right set, and the set is sorted using the natural ordering of
+     * element type. Neither input is mutated by this operation, an entirely new set is returned.
+     *
+     * @param left  the left set
+     * @param right the right set
+     * @param <T>   the type of the elements of the sets
+     * @return the sorted relative complement of the left set with respect to the right set
+     */
     public static <T> SortedSet<T> sortedDifference(Set<T> left, Set<T> right) {
         Objects.requireNonNull(left);
         Objects.requireNonNull(right);
diff --git a/core/src/test/java/org/elasticsearch/common/util/set/SetsTests.java b/core/src/test/java/org/elasticsearch/common/util/set/SetsTests.java
new file mode 100644
index 00000000000..9ef58c3acc7
--- /dev/null
+++ b/core/src/test/java/org/elasticsearch/common/util/set/SetsTests.java
@@ -0,0 +1,85 @@
+/*
+ * Licensed to Elasticsearch under one or more contributor
+ * license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright
+ * ownership. Elasticsearch licenses this file to you under
+ * the Apache License, Version 2.0 (the "License"); you may
+ * not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+
+package org.elasticsearch.common.util.set;
+
+import org.elasticsearch.common.collect.Tuple;
+import org.elasticsearch.test.ESTestCase;
+
+import java.util.HashSet;
+import java.util.Iterator;
+import java.util.Set;
+import java.util.stream.Collectors;
+import java.util.stream.IntStream;
+
+import static org.hamcrest.Matchers.equalTo;
+import static org.hamcrest.Matchers.greaterThan;
+
+public class SetsTests extends ESTestCase {
+
+    public void testDifference() {
+        final int endExclusive = randomIntBetween(0, 256);
+        final Tuple<Set<Integer>, Set<Integer>> sets = randomSets(endExclusive);
+        final Set<Integer> difference = Sets.difference(sets.v1(), sets.v2());
+        assertDifference(endExclusive, sets, difference);
+    }
+
+    public void testSortedDifference() {
+        final int endExclusive = randomIntBetween(0, 256);
+        final Tuple<Set<Integer>, Set<Integer>> sets = randomSets(endExclusive);
+        final Set<Integer> difference = Sets.sortedDifference(sets.v1(), sets.v2());
+        assertDifference(endExclusive, sets, difference);
+        final Iterator<Integer> it = difference.iterator();
+        if (it.hasNext()) {
+            int current = it.next();
+            while (it.hasNext()) {
+                final int next = it.next();
+                assertThat(next, greaterThan(current));
+                current = next;
+            }
+        }
+    }
+
+    /**
+     * Assert the difference between two sets is as expected.
+     *
+     * @param endExclusive the exclusive upper bound of the elements of either set
+     * @param sets         a pair of sets with elements from {@code [0, endExclusive)}
+     * @param difference   the difference between the two sets
+     */
+    private void assertDifference(
+            final int endExclusive, final Tuple<Set<Integer>, Set<Integer>> sets, final Set<Integer> difference) {
+        for (int i = 0; i < endExclusive; i++) {
+            assertThat(difference.contains(i), equalTo(sets.v1().contains(i) && !sets.v2().contains(i)));
+        }
+    }
+
+    /**
+     * Produces two random sets consisting of elements from {@code [0, endExclusive)}.
+     *
+     * @param endExclusive the exclusive upper bound of the elements of the sets
+     * @return a pair of sets
+     */
+    private Tuple<Set<Integer>, Set<Integer>> randomSets(final int endExclusive) {
+        final Set<Integer> left = new HashSet<>(randomSubsetOf(IntStream.range(0, endExclusive).boxed().collect(Collectors.toSet())));
+        final Set<Integer> right = new HashSet<>(randomSubsetOf(IntStream.range(0, endExclusive).boxed().collect(Collectors.toSet())));
+        return Tuple.tuple(left, right);
+    }
+
+}
\ No newline at end of file