Can a sentence end in an exclamation point and a question mark?
It depends on the context.
You cannot put them together in normal circumstances like: 'What the hell?!' .
However, here are some things that are accepted:
You can place the exclamation point immediately after the closing quotation mark in the case of a quotation ending with a question mark.
e.g. Stop asking, "Why me?"!
You can add a question mark after the closing quotation mark if there is quotation ending with an exclamation mark.
e.g. Who screamed, "The house is on fire!"?
You can place the exclamation point immediately after the question mark if there is a name or title of work ending with a question mark.
e.g. I can't stand Who's Afraid of Virginia Woolf?!
If there is a name or title of work ending with an exclamation point, then you may place the question mark immediately after the exclamation point.
e.g. Does he still work at Yahoo!?
So here are some ways in which you can put them together. I hope I helped.