Question

When you add 18 to one fourth of a number you get the number itself

Answer 1

N = number
....................................

n + 18 = n
4

n = n - 18
4

Cross Multiply

4 * ( n - 18 ) = n
4n - 72 = n
4n - n = 72
3n = 72
n = 72 
       3
n = 24

Answer 2

We can turn this into an equation. 
if x stands for the number you are looking for, then

18 + 1/4 x = x

we can solve this equation

18 + 1/4 x = x
subtract 1/4x from both sides
18 = 3/4 x
divide both sides by 3/4
24 = x