RSolve[{
g[n + 1] == g[n] + 10*(g[n]*Cos[-10 Degree] - y[n]*Sin[-10 Degree])/
Sqrt[(g[n]*Cos[-10 Degree] - y[n]*Sin[-10 Degree])^2 + (g[n]*Sin[-10 Degree] +
y[n]*Cos[-10 Degree])^2],
y[n + 1] == y[n] + 10*(g[n]*Sin[-10 Degree] + y[n]*Cos[-10 Degree])/
Sqrt[(g[n]*Cos[-10 Degree] - y[n]*Sin[-10 Degree])^2 + (g[n]*Sin[-10 Degree] +
y[n]*Cos[-10 Degree])^2],
g[0] == 100,
y[0] == 100}, {g[n], y[n]}, n]
When I run it I get the following error
Solve::ivar: "g[n]+(10(Cos[10]\g[n]+Sin[10]\y[n]))/Sqrt[(-g[<<1>>] Sin[<<1>>]+Cos[<<1>>] y[<<1>>])^2+(Cos[<<1>>] g[<<1>>]+Sin[<<1>>] y[<<1>>])^2] is not a valid variable."
I believe that it might be an error with my syntax, but I have no idea what it is.