The units digit of a digit-product equation

Let $P(n)$ denote the product of the digits of a number, and $S(n)$ denote the sum of the digits of a number. For example, $P(25) = 10$ and $S(25) = 7$ . Suppose $N$ is a two-digit number such that $N = P(N) + S(N).$ What is the units digit of $N$

Source: InternLM Lean-Workbook, record lean_workbook_plus_76401 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.