If your software is running on both machines, you can have one (or both) machines send out a particular broadcast (or, if you prefer, multicast) UDP packet on a specific port. Your program should also be listening on that same port. When it receives that packet (using recvfrom()), recvfrom()'s fifth argument will contain the IP address of the machine that sent the packet, i.e. the IP address you want.
(If OTOH your software is not running on the remote machine, you'll need to use some more general-purpose discovery mechanism such as mDNS or LLDP -- hopefully you won't have to do that, though, as it's a good deal more complicated)