set this up as an algebra problem with two equations
x+y=22 also written as x=22-y
x-y=10
substitute the first x into the second equation
(22-y)-y=10
22-2y=10
22-10=2y
12=2y
y=6
now plug in the known y into the first equation
x+6=22
x=22-6
x=16
now, let's check this
sum is 22=16+6 checks
difference is 10=16-6 checks
16 is the larger number
6 is the smaller number.
hope this helps.