First, let's call the two numbers we are looking for #n# and #m#.

We can then write:

#n + m = 8#

and

#n - m = 18#

First, solve the second equation for #n#:

#n - m + color(red)(m) = 18 + color(red)(m)#

#n - 0 = 18 + m#

#n = 18 + m#

Next, substitute #18 + m# for #n# in the first equation and solve for #m#:

#n + m = 8# becomes:

#(18 + m) + m = 8#

#18 + m + m = 8#

#18 + 2m = 8#

#-color(red)(18) + 18 + 2m = -color(red)(18) + 8#

#0 + 2m = -10#

#2m = -10#

#(2m)/color(red)(2) = -10/color(red)(2)#

#(color(red)(cancel(color(black)(2)))m)/cancel(color(red)(2)) = -5#

#m = -5#

Now, substitute #-5# for #m# in the solution to the second equation and calculate #n#:

#n = 18 + m# becomes:

#n = 18 + -5#

#n = 18 - 5#

#n = 13#

The two numbers are #13# and #-5#