The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?

Let the tens digit be a and the ones digit be b. The digits sum to 8, and the original number exceeds its reversal by 18, so 10a + b − (10b + a) = 18, which simplifies to a − b = 2. The digits 5 and 3 sum to 8 and differ by 2, so the original number is 53; its reversal, 35, is 18 less.

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