Something is driving your anxiety. Pinpoint that, and a solution will probably present itself. It might be a general fear of failure, anxiousness about working on the wrong thing, more immediate concerns about the problem being necessary for a job and food, .... All of those have different solutions.
One slightly more generic tip is that your task isn't to to solve the maybe unsolvable thing; it's to do a number of sub-tasks, learn more about it, communicate expectations to those who care, still schedule other important bits of your life despite a workload of unknowable magnitude, work on any essential backup plans, and so on. You have intermediate thoughts and actions between where you are and where you want to be. Focus there, and the fact that you're working on solvable problems might help.
A tangentially related idea -- math students often mistakenly assume the point of the homework is to figure out how to get it right. Rather, it's an opportunity to think through all the ways you can get it wrong and ingrain those so that in the future the right path forward is obvious. Failing to quickly solve the problem is the express point of the activity, and approaching the homework from the perspective of figuring out how to learn from it rather that how to get full marks tends to overcome a lot of mental hurdles and give you that latter benefit as a side effect. You're similarly, at least in the very near term, not actually working on getting the final solution; you're working on learning about the problem.
> One slightly more generic tip is that your task isn't to to solve the maybe unsolvable thing; ... learn more about it, communicate expectations to those who care
I have to go through this at least once a week in my support role, knowing a problem does not have an obvious solution or that it might but we have yet to find it - and not being able to necessary say that to the user in those words - 'setting expectation' and 'communicate expectations to those who care.
Often I find that this is often 'good enough' for the short to medium term, get them back up and working as best you can, show that you understand the issue even if you don't know the solution.
One slightly more generic tip is that your task isn't to to solve the maybe unsolvable thing; it's to do a number of sub-tasks, learn more about it, communicate expectations to those who care, still schedule other important bits of your life despite a workload of unknowable magnitude, work on any essential backup plans, and so on. You have intermediate thoughts and actions between where you are and where you want to be. Focus there, and the fact that you're working on solvable problems might help.
A tangentially related idea -- math students often mistakenly assume the point of the homework is to figure out how to get it right. Rather, it's an opportunity to think through all the ways you can get it wrong and ingrain those so that in the future the right path forward is obvious. Failing to quickly solve the problem is the express point of the activity, and approaching the homework from the perspective of figuring out how to learn from it rather that how to get full marks tends to overcome a lot of mental hurdles and give you that latter benefit as a side effect. You're similarly, at least in the very near term, not actually working on getting the final solution; you're working on learning about the problem.