Solution:

The number is 18, simply because
18 = 2 (1 + 8).

How does one find this number?

Let t be the digit in the tens place and u be the digit in the units place. Then, the number is 10 t + u, and the sum of its digits is t + u. The following equation can be readily written:

10 t + u = 2 t + 2 u or
8 t = 1 u.

Thus, t / u = 1 / 8. Since t and u are digits, t must be 1 and u must be 8.

Food for thought:

Is the assumption of a 2-digit number a valid one?