28. In response to a question about his age, the grandfather answered: “The number expressing my age in years is a two-digit number equal to the sum of the number of its tens and the square of its units.” How old is the grandfather?
28. Let the grandfather be $(10 a+b)$ years old. Then $10 a+b=a+b^{2}$, hence

$$
9 a=b^{2}-b, \text{ or } a=\frac{b(b-1)}{9}
$$

Since $a$ and $b$ are single-digit numbers, the equality holds only when $b=9$. In this case, $a=8$. Therefore, the grandfather is 89 years old.