In order to play with friends on the same network you need to turn the Anti-cheat setting to off when creating a game.

You see that the description of anti cheat explains that users sharing a connection will be banned from logging in to the same game.
Each player will have received these messages and should reply to them. Proof that you are unique individuals starts by responding and showing that you are a live person at the end of the email, not a fake email acccount created to cheat. It is a dialog with the support staff, it is not like you are applying for top secret security clearance or anything. If you each have a long history and have not triggered the anticheat system before, then that is a good sign as well.
If you are unable to reply to a message you may choose ONE of the following methods to resolve the issue:
1) Post in this thread: https://forum.callofwar.com/index.php?thread/16355-help-my-account-has-been-banned/&postID=125254#post125254
Or
2) create a support ticket using this link: https://www.callofwar.com/index.php?id=279
Do NOT do both. This wastes time sorting out duplicate and triplicate reports. If you have already replied to a message or created a support ticket just be patient. This process will take days.
Once you do get your account straightened out be very sure not to play together in a regular game from the same connection, unless anti-cheat is set to "no" or "disabled"