I don't know how you are going to do this.
Obviously, you can set a shutdown time easily enough - when your computer starts, you should also get it to run a bash script which contains your shutdown command (see man (8) shutdown).
The following has to be run as root unless you give yourself sudo permissions. (man sudo)
#### Shutdown code
sudo shutdown 22:00 The system is going to shutdown automagically at 10pm!
cp /etc/nologin nologin_backup
This would probably need to be run in the background to avoid wasting a terminal.
Also, I do not vouch for how safe deleting the /etc/nologin file is - this is created if the shutdown command is issued with any kind of delay, whether a countdown or a preset time, and it's purpose is to not allow anyone to log in once a shutdown command has been issued. You might be ok if this script is run from your .bashrc or .bashprofile, as these are executed once you login, so as long as you don't log out before 10pm you're fine.
As for booting at a specific time - I have no idea unless you can do it through some kind of suspend/resume function, rather than a complete shutdown.
I suppose you can always set an alarm clock for 8:00am and then train your cat to press the power button!