Scanning An External Network Through UDP / ARP Scan?

the setup is as follow: I have two separate network.192.168.90.xx and 10.10.xx.xx the two boxes being connected via an ethernet cable. How would I go about having a 192.(...) machine speak to a 10.(...) box? My boss tells me that via a UDP call the 192.(...) machine can get the IP of a 10.(...) box. Isn't UDP dependant on a subnet mask to limit the # of queries, and in that case would it even be feasable? I was thinking instead of spoofing the 192.(...) IP to an unoccupied 10.(...) IP. Of course to do this would require knowing what IPs are unoccupied on the other network, and I cannot assume the would respond to pings.