Winner's Curse After Seeing High Against One Low Signal

An asset has common value $V\in\{0,100\}$ with prior $P(V=100)=1/2$. Each bidder receives a signal that equals the true state with probability $0.8$, independently across bidders conditional on $V$. You observe a high signal and learn that your rival observed a low signal. What is $E[V\mid \text{your signal high, rival low}]$? If you bid $80$ in a first-price auction and win for sure in this information set, what is your expected profit?