Question 132353
First number: x
Second number: y

The sum of the two numbers:  x + y
The difference of two numbers: x - y


So:
{{{x+y=18}}}
{{{x-y=10}}}


Add the two equations:
{{{2x-0y=28}}}


Divide by the coefficient on x:
{{{x=14}}}


{{{14+y=18}}}
{{{y=4}}}


One of the numbers is 14, and the other number is 4.  Check:  The sum of 14 and 4 is 18, and their difference is 10.  Answer checks.