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

From the problem, we know that $x^{2}-4 x=y, y^{2}-4 y=x$. Adding the two equations gives $x^{2}+y^{2}=5(x+y)$, and subtracting the two equations gives $x^{2}-y^{2}=3(x-y)$. Given that $x \neq y$, we know that $x+y=3$. Therefore, $x^{2}+y^{2}=5(x+y)=15$.