2014 CFA Mock 1, "Li" Vignette Q3

Does anyone know how to calculate the Var(E) term in this question? The solution says it is equal to 0.0770. However I am not sure how this number if determined and do not see it listed in the vignette.

0.2704 = b1^2*VAR(F1) + b2^2*VAR(F2) + 2 b1 b2 COV(F1,F2) + VAR(E)

Cov (F1, F2) initally is 0 because of zero correlation.

so 0.2704 = 1.02^2 * 0.0784 + 1.045^2 * 0.1024 + VAR(e)

VAR (e) = 0.0770

Makes sense. Thank you!

I believe this equation has an alpha term in the front-right?

Can you explain why we use the same error term after changing the corr from 0 to 0.25

is the error term anywhere dependent on the correlation term?