assume that the larger number is m and the smaller one is n.
the larger is 10 less than twice the smaller, this means that:
m = 2n-10
the sum of the two is 38, this means that:
m+n = 38
substitute by the first equation in the second one:
2n-10+n=38
3n=48
n= 16
substitute by n in the first equation:
m=2n-10=2(16)-10= 22
based on this,
the larger number is 22 while the smaller number is 16