This is not a rhetorical question (because no one knows the answer). It is kind of like a dilemma in that it's difficult to answer; however, it does not quite fall under a "what is the meaning of life" category of questions where the answer is highly subjective.
Perhaps what you face is an enigma?
Probably a mystery:
an unexplained or inexplicable event, phenomenon, etc
something that is not fully understood or that baffles or eludes the understanding; an enigma: How he got here is a mystery.
To take cue from your own comment
A confusing and difficult problem or question.
1.1 A question asked for amusement, typically one with a pun in its answer; a riddle
Although a conundrum usually has an answer I might suggest
Unable to be explained or accounted for.
Not confirmed; unknown.
In the field of education we refer to unanswerable questions as "essential questions" and encourage teachers to plan units around them. Examples include "what are the limits of arithmetic?" or "Who is responsible for the atrocities of previous generations?"
It's not that they cannot be answered, but that there is no "right" or "wrong" answer. Just theories that students construct and interrogate.
It depends entirely on the context. I'm only 13 so this may be false, but it is not 'a' word, normally it would be an inexplicable question but if you're talking about a question that is simply impossible to answer but it seems like their should be an answer it is a dilemma
paradoxial ? a question in which the answers are contradictory.