Let x and (16-x) represent the original ten and units digits respectively

Reversing its digits increases the number by 18

Set up the relational equation

[10x + (16-x)] + 18 = 10(16 - x) + x

Solving for x

9x + 34 = 160 - 9x

Combine like terms

18x = 126

Divide each side of the equation by 18

18x/18 = 126/18

x = 7

So 16 - x = 16 - 7 = 9

The first number is 79, the other number is 97. and 97 - 79 = 18 so we match up.

The number in our answer is

**79**