Find the absolute value of the product of the two possible values for \(f(10)\) given that
\[f(xf(x)+f(y))=y+f(x)^2\]
where \(x, y \in \mathbb{R}\) and \(f(x)\) is a polynomial function.
Note: This question has been edited several times, and is now correct.
See Part I if you enjoyed this problem! :D