Whilst solving a problem, the following system of non-linear equations arose:

$$0= \frac{1}{x^2}-\frac{1}{(y-x)^2}-\frac{1}{(1-x)^2}$$

$$0= \frac{1}{y^2}+\frac{1}{(y-x)^2}-\frac{1}{(1-y)^2}$$

I have tried to solve it via brute force and by trying to add them both in a way that could give me the answer, but I still haven't got it.

I can't manage to find the intersection of the two parametric equations that these equations give. I know that I can find approximate solutions with the Wolfram Alpha tool, but I would like to know, if any, an analytical or strong numerical way to proceed.

**Note:** Out of all the solutions ($8$ it seems, $4$ real and $4$ complex), I only need the one that takes real values for $x$ and $y$, with $0<x<y<1$.