Solve z=arctanx+y/x-y

$$z = \arctan \frac { x + y } { x - y }$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{y\left(\sin(z)+\cos(z)\right)}{\cos(z)-\sin(z)}\text{, }&\nexists n_{3}\in \mathrm{Z}\text{ : }\left(z=\pi n_{3}+\frac{\pi }{2}\text{ or }z=\pi n_{3}+\frac{\pi }{4}\right)\text{ and }y\neq 0\text{ and }|z|\leq \frac{\pi }{2}\\x\neq 0\text{, }&y=0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }z=\pi n_{2}+\frac{\pi }{4}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }z=\pi n_{1}+\frac{\pi }{2}\text{ and }|z|\leq \frac{\pi }{2}\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{x\left(\cos(z)-\sin(z)\right)}{\sin(z)+\cos(z)}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(\left(z>\pi n_{2}+\frac{3\pi }{4}\text{ and }z<\pi n_{2}+\frac{3\pi }{2}\right)\text{ or }\left(z>\pi n_{2}+\frac{\pi }{2}\text{ and }z<\pi n_{2}+\frac{3\pi }{4}\right)\right)\text{, }n_{2}=-1\text{ and }x\neq 0\\y\neq 0\text{, }&x=0\text{ and }\exists n_{3}\in \mathrm{Z}\text{ : }z=\pi n_{3}+\frac{3\pi }{4}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }z=\pi n_{1}+\frac{\pi }{2}\text{ and }|z|\leq \frac{\pi }{2}\end{matrix}\right.$$