Wireless Network and Wired LAN on different subnets

Hi all,
I am in the position of being the "network admin" in a small shop of 20
workstations and 4 servers, in addition to multiple other duties (including
programming). I have no formal training in Windows networking but have
gotten by so far with 1 Domain and one subnet on our Wired LAN.

We recently added a FortiWIFI 60 network appliance that I have configured to
work with the Wired LAN just fine. It acts as our Router, Firewall and DSL
connection to the internet for our entire shop.

The problem occurs when I try to connect a wireless laptop to the WLAN
interface on the FortiWIFI.
Fortinet does NOT allow the Wireless LAN and the Wired interface to be on
the same subnet. Therein lies the problem (I think).

After 2 hours on the phone with Fortinet tech support, I now have my
wireless laptop connected to the network, can access the Internet and can
only PING other machines on the wired LAN by IP address.

However, I can't get the other wired computers to show up in Windows
Explorer or network neighborhood.

How do I reconcile 2 different subnets so that the wired computers show up
in Windows Explorer on the wireless laptop and vice versa. It may be a
simple thing for the MVPs, but I have not encountered this situation before,
and I have a programming job due in 2 days and don't have a lot of time for
"higher education".

The primary DC is a Windows 2003 SBS.

Any help would be appreciated.
Thanks............