Solve S=(sqrt{x-sqrt{x^2-t}})-0.02

$$S = ( \sqrt { x - \sqrt { x ^ { 2 } - t } } ) - 0.02$$

Solve for S (complex solution)

$$S=\sqrt{-\sqrt{x^{2}-t}+x}-0.02$$

Solve for t (complex solution)

$$t=\left(S+0.02\right)^{2}\left(-\left(S+0.02\right)^{2}+2x\right)$$

$$\left(arg(-\left(S+0.02\right)^{2}+x)<\pi \text{ and }arg(S+0.02)<\pi \right)\text{ or }\left(arg(x)<\pi \text{ and }S=-\frac{1}{50}\right)\text{ or }\left(x=\left(S+0.02\right)^{2}\text{ and }arg(S+0.02)<\pi \right)\text{ or }\left(x=0\text{ and }S=-\frac{1}{50}\right)$$

Solve for S

$$S=\sqrt{-\sqrt{x^{2}-t}+x}-0.02$$

$$\left(x=0\text{ and }t=0\right)\text{ or }\left(x>0\text{ and }t\geq 0\text{ and }x\geq \sqrt{t}\text{ and }t\leq x^{2}\right)$$

Solve for t

$$\left\{\begin{matrix}\\t=0\text{; }t=0\text{, }&\text{unconditionally}\\t=\left(S+0.02\right)^{2}\left(-\left(S+0.02\right)^{2}+2x\right)\text{, }&S\geq -\sqrt{2x}-\frac{1}{50}\text{ and }S\leq \sqrt{2x}-\frac{1}{50}\text{ and }x>0\text{ and }-\left(S+0.02\right)^{2}+x\geq 0\text{ and }S+0.02\geq 0\end{matrix}\right.$$