let 'a' represent one number and 'b' the other

we assume that b < a

b+a = 21, so a=21-b

b-a = 13

we substitute 'a' with '21-b' in the second equation:

b-(21-b) = 13

2b = 34

b = 17

17-a = 13

a = 4

the numbers are 4 and 17