First, let's give the two numbers a name:
Number 1: we will call: #n#
Number 2: we will call: #m#
From the information in the problem we can write these two equations:
Equation 1: #n + m = 17#
Equation 2: #n - m = 29#
Step 1 Solve the first equation for #n#:
#n + m = 17#
#n + m - color(red)(m) = 17 - color(red)(m)#
#n + 0 = 17 - m#
#n = 17 - m#
Step 2 Substitute #(17 - m)# for #n# in the second equation and solve for #m#:
#n - m = 29# becomes:
#(17 - m) - m = 29#
#17 - 1m - 1m = 29#
#17 + (-1 - 1)m = 29#
#17 + (-2)m = 29#
#17 - 2m = 29#
#-color(red)(17) + 17 - 2m = -color(red)(17) + 29#
#0 - 2m = 12#
#-2m = 12#
#(-2m)/color(red)(-2) = 12/color(red)(-2)#
#(color(red)(cancel(color(black)(-2)))m)/cancel(color(red)(-2)) = -6#
#m = -6#
Step 3 Substitute #-6# for #m# in the solution to the first equation at the end of Step 1 and calculate #n#:
#n = 17 - m# becomes:
#n = 17 - (-6)#
#n = 17 + 6#
#n = 23#
The Two Numbers Are: #23# and #-6#