Could you provide information on your wireless connection? If you are using a wireless NAT router, you can have the wired connection on a subnet and use forwarding. If your router is a nat router, you don't need to configure masquerading on the first computer (with wireless). The router can do it.
I did this once to share wireless connection on my laptop, for my desktop. You need to enable ip forwarding. I found that I also needed to load the conntrack module to get it to work. (was called ip_conntrack but now is called nf_conntrack)
You may be able to enable ip forwarding in your distro's device configuration, or in a boot up script that includes the line:
echo 1 >/proc/sys/net/ipv4/ip_forward