That's 'almost' what the OP had done, after I asked him to measure L-E at the 'non-working' ("208V") socket....Easy to check, measure L - N and L - E at both sockets.
We know that the non-working socket has 208V L-N and 241V L-E. We also know that the working socket has 240V L-N, and I would be very surprised if L-E at that one is not similar (i.e. around 240-241V).
Kind Regards, John