Madness at the Darkmoon Faire Cards List & Guide
This may seem like a silly question but I cannot easily find a way to log out of this accidental account to then log back into my usual account I use on desktop.
I'm guessing you're asking about the site and not the game?
Yes, I've just encountered the same problem!
There's no obvious logout option anywhere!
Note this is on the mobile site. Desktop site is fine