Cross Subnet Connections

Hope this isn't a stupid question!

I have a large private network with several subnets operating on it.
They are in the 10.x.x.x ranges. I have a central proxy that gives connections to the internet on one subnet, which all the others can connect to. I then have two computers, one with ip address 10.4.2.52 and one with ip 10.5.2.76.
These two computers are both able to access the internet through the proxy, but they cannot communicate directly with each other. I am planning to make an application that would require either tcp or udp communication between them, however, i do not have access to the proxy or any of the routers! Is there a way of making a connection between them, or is it simply impossible.

George
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