let 'x' represent one number and 'y' represent the other, then their reciprocals are '1/x' and '1/y', respectively

x + y=9, or y=9-x

1/x + 1/y = 2

substituting 'y' with '9-x' in the second equation:

1/x + 1/(9-x) = 2

solving for 'x' we have x= (3*sqrt(7)+9)/2 = 8.47

...y eventually solves to approximately 0.53

given this information, the answer is approximately 8.47 and 0.53 but there is some error in the problem statement since these types of problems should produce simple integer answers