Because of the default settings in several Linux Distros you will not be able to use F10 to exit Midnight Commander. However the solutions is simple.
I use Linux Mint Debian Edition for most of my Linux Desktop usage. And I belive it is the same issue with F10 opens a menu instead of closing Midnight Commander in several other Distros as well.
How to fix it
This is how you can start using F10 to close Midnight Commander. First open the Terminal. In the menu go to Edit and select Preferences. In the preferences window uncheck the options that says “Enable the menu accelerator key”.
Now to need to close the terminal and open it again for the change to take effect. Now you should be able to use F10 to close MC. Enjoy your F10 and MC.