hey so i have this equation i need to manipulate to solve for F- concentration.

E1 = constant - 0.05916log[F]
E2 = constant -0.05916log([F]+[Spiked])

E2-E1=-0.05916log(F+S) + 0.05916log[F]

E2-E1/0.05916) = log[F+S] + log[F]

how do I solve for log[F] ???

Your first line E2-E1. You dropped a negative sign on the first term.

-log(F+S)+logF
log (F/(F+S))