So I have a problem and I was hoping for some insight.

I figured out how to get
(surd(n, x)-surd(n, y))

without knowing x or y, (only n), through a convergent series of approximate identities.
n is the product of x and y, where x<y

My only issue is I don't know where to go from here. I've basically hit the limit of my insight into the problem.

surd() here is just a function that returns the results of two arguments, a, b, such that (a^2)-b.
Both are guaranteed to be positive integers, greater than 1.

But, having come this far, with a couple pages of intermediate identities, I'm at a loss.