2001 AMC 12 Question 2

Let $P(n)$ and $S(n)$ denote the product and the sum, respectively, of the digits of the integer $n.$ For example, $P(23) = 6$ and $S(23) = 5.$ Suppose $N$ is a two-digit number such that $N = P(N) + S(N).$ What is the units digit of $N?$