What is an absolute value equation with the solutions of x=8 and x=18

| x-13| = 5    

Step-by-step explanation:

(We need an absolute value equation with solutions of 8 and 18

| x-y| = z

We get a positive and negative solution

x-y =z     x-y = -z

Solve for x

Add y to each side

x-y+y = z+y             x-y+y = -z+y

x = z+y                    x = -z+y

Let the larger one equal 18 and the smaller one equal 8

z+y = 18   and -z+y = 8

Add the two equations together to eliminate z

z+y = 18  

-z+y = 8                

2y = 26

y = 13

Now we need to find z

z+y = 18

z+13 = 18

z = 18-13

z=5

   Putting this back into the absolute value equation

| x-13| = 5