Solve left|x-left(4^2y+1right)^2/4^2+yright|={left(1/2right)}^2

$$\left| x- \frac{ { \left( { 4 }^{ 2y+1 } \right) }^{ 2 } }{ { 4 }^{ 2+y } } \right| = { \left( \frac{ 1 }{ 2 } \right) }^{ 2 }$$

Solve for x

$$x=64^{y}-\frac{1}{4}$$

$$x=64^{y}+\frac{1}{4}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{\log_{2}\left(x-\frac{1}{4}\right)}{6}\text{, }&x>\frac{1}{4}\\y=\frac{\log_{2}\left(x+\frac{1}{4}\right)}{6}\text{, }&x>-\frac{1}{4}\end{matrix}\right.$$