$a=\left(\sqrt{x}+\sqrt{y}\right)^{2}$
$x\geq 0\text{ and }y\geq 0$

$x=\left(\sqrt{y}-\sqrt{a}\right)^{2}$
$y\geq 0\text{ and }a\geq 0\text{ and }-\left(\sqrt{y}-\sqrt{a}\right)\geq 0$

$a=\left(\sqrt{x}+\sqrt{y}\right)^{2}$
$\left(x=0\text{ and }y=0\right)\text{ or }arg(\sqrt{x}+\sqrt{y})<\pi $

$x=\left(\sqrt{y}-\sqrt{a}\right)^{2}$
$y=a\text{ or }arg(\sqrt{y}-\sqrt{a})\geq \pi $