|To make RDC work properly you will need to know your brother's external IP address. He can easily find this out by going to the What's My IP web site.|
You use that IP in RDC to connect to him.
A couple of considerations:
1) He will need to allow you to connect remotely. To do this, he will have to go into Control Panel >> System and click on the Remote Tab. Once there, he has to check the "Allow users to connect remotely to this computer" box.
2) If he has a SOHO router he will have to create a "port forward" for port 3389 (RDC) and point it to the LAN IP of the PC you will be connecting to. If he has a software firewall, he'll have to allow that same port number to connect.