A problem is open to a solution. That what makes it a problem.
A paradox, on the other hand, is gated by boundaries that make a solution impossible.
If you've been working on a situation, chewing on it, throwing everything you've got at it, it might not be a problem at all. You may have invented a paradox, creating so many limits that you'll never get anywhere.
It makes no sense to work on a paradox. Drop it and move on. Even better, figure out which boundaries to remove and turn it into a problem instead.
Two examples: Building a worldwide limo fleet is impossible, a paradox that requires too much money and too much time–by the time you raised enough money and hired enough supervisors, you'd never be able to charge enough to earn it back. But once you ease the boundary of, "if you own a transport service, you must own the cars and hire the drivers," the idea of building a network is merely a problem.
Another more general one: Making significant forward motion without offending anyone or exposing yourself to fear is a paradox. But once you're willing to relax those boundaries, it becomes a problem, one with side effects you're willing to live with…