Answer: The two numbers are 151 and 66.
Step-by-step explanation: We are to find the two numbers whose sum is 217 and difference is 85.
Let, 'x' and 'y' represents the two numbers, where x > y.
Then, according to the given information, we have

Adding equations (i) and (ii), we get

and from equation (i), we get

Therefore, x = 151 and y = 66.
Thus, the two numbers are 151 and 66.