A trivial solution for any equation of the form pq−qp=n is p=n+1,q=1. However, these solutions are obviously uninteresting. We are looking for solutions with p,q>1.
Just by trying out a few small numbers I easily found one non-trivial solution:
37−73=1844
There may be other solutions, since I have not proven that this is the only non-trivial solution.
In general, the equation pq−qp=n is an exponential Diophantine equation, and no general method is known for solving this type of equations.
I think it's safe to assume that there is no closed-form non-trivial general solution p(n),q(n) that works for any n. In fact, I'm not sure there even is a solution for any n, but again, this statement needs to be proven.
For a specific n it's very easy to write code (for example in Mathematica) that will find a solution if it exists and if the numbers involved are small enough.
An expert in number theory will probably have much more to say on this subject :)
Say....if you do the same thing I showed you, that might help you with your homework. :)