A dilemma is a difficult choice between unattractive alternatives. A problem is a situation that must be resolved somehow.
When the prototype did not perform to specifications, we
were faced with the dilemma of abandoning the
project and losing all the resources we had invested in it to
date or going ahead with the project and having no guarantees of
any future returns.
Jane described the problem we were having in
the waste water treatment facility.
Do not use dilemma in place of problem.
Can you find a solution for our
dilemma?
Can you find a solution for our
problem?
[We don't have any solutions
right now.]
Can you find a way out of our
dilemma?
[We have some solutions right
now, but none are attractive.]