Maybe your edge router supports a VPN? check the docs. If not, without changing your edge router, one possibility is to buy a couple of inexpensive routers, install a VPN build of ddwrt or openwrt. Then use OpenVPN or IPSEC. I prefer OpenVPN as it's easier to set up.
You can install the routers behind other firewalls. You'll need to ensure the firewall allows the VPN traffic. And, on the server end or the router that runs the OpenVPN server you'll need to ensure that the firewall at that end has a hole poked in it from the source ip of your other branch office so that it can link up.
Then at both ends, put a static route to the foreign network to point to the new VPN router.
I have done this a couple of years ago and it worked great. You do have to watch that the private IP ranges of both networks are different though.
Also, it'd be helpful to add a DNS server to the branch office network to reach the servers at the head office by their private IP. If you happen to have a local domain controller then that should be easy. Don't even think about putting the domain controller for the branch office on the other side of the VPN. Your users will hate you if you do that. Seen that done before... yuck!
If you need higher performance, considering using Mikrotik routers with RouterOS. They are also very innexpensive and may be a bit quicker. Although there are some quite fast asus routers that work really well under OpenWRT.
It's hard to know what's best really because you haven't said anything about the existing equipment.