Let the two numbers be x and y such that x>y. The sum of these two numbers is (x+y) and the difference is (x-y).

Therefore, by the condition of the question,

x+y=8.......(1)

x-y=10......(2)

Adding (1) and (2), we have, 2x=18, or x=9.

Subtracting (2) from (1), we have, 2y=-2, or, y=-1.

Therefore, the two numbers are -1 and 9.