defining an implicit function

Questions
1

I’d like to do some GR calculations with the Kruskal-Szekeres coordinates and the Schwartzchild metric (or other metrics). I have the RGTC package, but I don’t know how to define the metric with r, which is an implicit function of u and v (r/2M-1) Exp[r/2M]=u^2-v^2. Any way to define implicit functions in Mathematica?