The sum of two numbers is nine if one number is subtracted from the other the result is -1 find the numbers

Lets make x and y the two numbers. The sum of the two numbers (x and y) is 9 means that they add to 9. So the first equation is 

x+y = 9

Let's isolate y by subtracting x from both sides. That gives us

y = 9-x

The other bit of information given is "if one number is subtracted from the other, the result is -1", which means we have this other equation

x-y = -1

From here, substitute y for 9-x

x-y = -1
x-(y) = -1
x-(9-x)=-1
x-9+x=-1
2x-9 = -1
2x-9+9 = -1+9
2x = 8
2x/2 = 8/2
x = 4

If x = 4, then y is...
y = 9-x
y = 9-4
y = 5

Therefore, the two numbers are 4 and 5. They add to 9
4+5 = 9
and they subtract to -1
4-5 = -1

Final 4 and 5