UKMT Cayley Olympiad, 2025

A number $N$ is a two-digit positive integer. It can be written as $\overline{ab}$ to show its digits $a$ and $b$. How can $N$ written in terms of $a$ and $b$ in standard algebra? Find all possible $N$ with digits $a$ and $b$, where $N = \overline{ab}$ and $N = a + b^2$.