The difference between two numbers is 5, and twice the smaller number is 18 more than the larger number. find the numbers.

Let's write it down in mathematical terms:

x-y=5
so
x=5-y

this means:difference between two numbers is 5

2y=x+18

this means: twice the smaller number is 18 more than the larger number
and we can substitute the x for what we said before:

2y=(5-y)+18

we add 1 y from each side:

3y=5+18

3y=23

so the smaller number is 23 and the bigger number is 23+5=28.