22. A two-digit number, the sum of the unit digit and the tens digit plus their product equals this two-digit number. Then the unit digit of this two-digit number is ( ).
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
22. E.

Let this two-digit number be $10a + b$, where $a, b \in \mathbf{Z}, 0 \leqslant a, b \leqslant 9, a \neq 0$.
Then $10a + b = ab + a + b \Rightarrow a(b-9) = 0$. Since $a \neq 0$, it follows that $b = 9$.