According to the the Oxford Learner’s Dictionary, the "e" is optional when a word ends in "-dg(e)ment".
Dictionary examples:
... And some other similar examples from the internet:
- ledg(e)ment
- lodg(e)ment
- grudg(e)ment.
Of these, only judgment is explicitly said to be found "especially in North American English"; regional distinctions don't seem to play a role in any of the other options.
Is this statement verifiable? What is the evidence, and how widespread is the variation? Is there a historical reason for judgment being unique in this sense? (If it even is unique...)