Question

Rewrite R=X^2 + Y^2 for Y

Answer 1

$R = X^{2} + Y^{2}$

$Y^{2} = R - X^{2}$

$Y = \sqrt{R - X^{2} }$

Answer 2

$R=X^2 + Y^2\\ Y^2=R-X^2\\ Y=\sqrt{R-X^2}$

That, assuming all the variables are non-negative numbers.

Otherwise, there's one more soultion:

$Y=-\sqrt{R-X^2}$