Let x represent the larger number.
Let y represent the smaller number
One number is 17 more than another number. It means that
y + 17 = x
The sum of the numbers is 41. It means that
x + y = 41
Substituting x = y + 17 into x + y = 41, it becomes
y + 17 + y = 41
y + y = 41 - 17
2y = 24
y = 24/2
y = 12
x = 17 + 12
x = 29
The numbers are 29 and 12