First, let's name the two numbers #n# and #m#.

Then we can write:

#n + m = 48#

and

#n - m = 24#

Step 1) Solve the first equation for #n#:

#n + m = 48#

#n + m - color(red)(m) = 48 - color(red)(m)#

#n + 0 = 48 - m#

#n = 48 - m#

Step 2) Substitute #48 - m# for #n# in the second equation and solve for #m#:

#n - m = 24# becomes:

#48 - m - m = 24#

#48 - 2m = 24#

#-color(red)(48) + 48 - 2m = -color(red)(48) + 24#

#0 - 2m = -24#

#-2m = -24#

#(-2m)/color(red)(-2) = (-24)/color(red)(-2)#

#(color(red)(cancel(color(black)(-2)))m)/cancel(color(red)(-2)) = 12#

#m = 12#

Step 3) Substitute #12# for #m# in the solution to the first equation at the end of Step 1 and calculate #n#:

#n = 48 - m# becomes:

#n = 48 - 12#

#n = 36#