Opening modifier "Exceeding even the figures predicted by the most optimistic financial analysts" modifes earnings and not company.
How to find this?.
One way-Company exceeds the figures predicted by analysts-Illogical comparison.
Other way- See the word "figures" ...so for logical comparison, we need other thing which can be expressed in figures...and that’s " earnings" and not company for sure
So eliminate A, B, and C.
Between D and E, the only difference is "those of" at the end of E (absent from D). So you ask yourself "what is being compared here?" The earnings in one quarter to the earnings in another quarter. The earnings to the earnings. So I have to mention both sets of earnings, even if I use some sort of pronoun or other referent the second time (which is what the test usually does).
D says the "earnings were more than double the quarter" - that's not the right comparison.
E says the "earnings were more than double the (other) earnings" - that's the right comparison.
Hence E.