Solve E=4ab/frac{x^2-2xy+y^2+2xy{-4ab}}

$$E = \frac{ 4ab }{ \frac{ { x }^{ 2 } -2xy+ { y }^{ 2 } +2xy }{ -4ab } }$$

Solve for E (complex solution)

$$E=-\frac{16\left(ab\right)^{2}}{x^{2}+y^{2}}$$

$$x\neq iy\text{ and }x\neq -iy\text{ and }b\neq 0\text{ and }a\neq 0$$

Solve for a (complex solution)

$$a=-\frac{i\sqrt{E}\sqrt{x^{2}+y^{2}}}{4b}$$

$$a=\frac{i\sqrt{E}\sqrt{x^{2}+y^{2}}}{4b}\text{, }x\neq iy\text{ and }x\neq -iy\text{ and }b\neq 0\text{ and }E\neq 0$$

Solve for E

$$E=-\frac{16\left(ab\right)^{2}}{x^{2}+y^{2}}$$

$$\left(y\neq 0\text{ or }x\neq 0\right)\text{ and }b\neq 0\text{ and }a\neq 0$$

Solve for a

$$a=\frac{\sqrt{-E\left(x^{2}+y^{2}\right)}}{4|b|}$$

$$a=-\frac{\sqrt{-E\left(x^{2}+y^{2}\right)}}{4|b|}\text{, }\left(y\neq 0\text{ or }x\neq 0\right)\text{ and }b\neq 0\text{ and }E<0$$