It's a anal "Donkey Punch" and as your partner lays out cold, you finish it off with a "Dirty Sanchez" by rubbing your dick across thier upper lip". Invented by a guy name Erik. Thus the name Dirty Donkey-E.
Police investigators where perplexed when they found a girl out cold with her pants down wearing a shit mustashe. They came to the conclusion that she had given the Dirty Donkey-E.