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#
