2 questions regarding solutions for $\sqrt{a+b} - (a-b)^2 = 0$ Here's two questions derived from the following question:
$\quad\begin{matrix}
\text{Is there more than one solution to the following statement?} \\
\!\sqrt{a+b} - (a-b)^2 = 0 
\end{matrix}$
$\color{Blue}{(1)\!\!:\;}$How would one (dis)prove this? I.e. In what ways could one effectively determine whether an equation has more than one solution; More specifically, this one?
$\color{Blue}{(2)\!\!:\;}$Is it possible to determine this with(out) a valid solution as a sort of reference? 
Cheers!

We can rearrange to $$a+b=(a-b)^4$$
There are hence infinitely many solutions.  For example, take $a+b=2^4=16$.  Then $a-b=2$.  We solve this to get $a=9, b=7$.  Or take $a+b=3^4=81$.  Then $a-b=3$.  We solve this to get $a=42, b=39$.
