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#