To keep it simple, I'm going to refer to the element as element X. We know that element X has two possible isotopes, which I'm going to call X_1 and X_2.
We know the average mass of element X is 141.8, the mass of X_1 is 148.6, and that 41.11% of element X is found to be X_1. This also tells us that the other percentage of element X is 100 - 41.11 = 58.89%.
Now knowing all of this information, we can set up a formula to solve for the mass of X_2, as the average mass of element X is 41.11% the mass of X_1 and 58.99% the mass of X_2:
"Average Mass" = .4111xxX_1 + .5899xxX_2
141.8 = .4111xx148.6 + .5899xxX_2
Now all we do is solve for X_2, yielding
X_2 = (141.8 - .4111xx148.6)/(.5899) = 136.8 " amu"
We can double check our work by plugging in values for X_1 and X_2 and making sure that they average out to 141.8:
.4111xx148.6 + .5899xx136.8 = 141.8" amu"