AMC 10 2015a Problem 16

If $y+4 = (x-2)^2, x+4 = (y-2)^2$, and $x \neq y$, what is the value of $x^2+y^2$? $\textbf{(A) }10 \textbf{(B) }15 \textbf{(C) }20 \textbf{(D) }25 \textbf{(E) }\text{30}$

Video Solution by MegaMath (LaTeX) https://www.youtube.com/watch?v=L54A79X1ezc&t=2s