Remove Elements from a HashSet while Iterating

The reason you get a ConcurrentModificationException is because an entry is removed via Set.remove() as opposed to Iterator.remove(). If an entry is removed via Set.remove() while an iteration is being done, you will get a ConcurrentModificationException. On the other hand, removal of entries via Iterator.remove() while iteration is supported in this case.

The new for loop is nice, but unfortunately it does not work in this case, because you can't use the Iterator reference.

If you need to remove an entry while iteration, you need to use the long form that uses the Iterator directly.

for (Iterator<Integer> it = set.iterator(); it.hasNext();) {
    Integer element = it.next();
    if (element % 2 == 0) {
        it.remove();
    }
}

You can manually iterate over the elements of the set:

Iterator<Integer> iterator = set.iterator();
while (iterator.hasNext()) {
    Integer element = iterator.next();
    if (element % 2 == 0) {
        iterator.remove();
    }
}

You will often see this pattern using a for loop rather than a while loop:

for (Iterator<Integer> i = set.iterator(); i.hasNext();) {
    Integer element = i.next();
    if (element % 2 == 0) {
        i.remove();
    }
}

As people have pointed out, using a for loop is preferred because it keeps the iterator variable (i in this case) confined to a smaller scope.

you can also refactor your solution removing the first loop:

Set<Integer> set = new HashSet<Integer>();
Collection<Integer> removeCandidates = new LinkedList<Integer>(set);

for(Integer element : set)
   if(element % 2 == 0)
       removeCandidates.add(element);

set.removeAll(removeCandidates);

Java 8 Collection has a nice method called removeIf that makes things easier and safer. From the API docs:

default boolean removeIf(Predicate<? super E> filter)
Removes all of the elements of this collection that satisfy the given predicate. 
Errors or runtime exceptions thrown during iteration or by the predicate 
are relayed to the caller.

Interesting note:

The default implementation traverses all elements of the collection using its iterator(). 
Each matching element is removed using Iterator.remove().

From: https://docs.oracle.com/javase/8/docs/api/java/util/Collection.html#removeIf-java.util.function.Predicate-