Your best source for help might be your own IT department that manages the building LAN. Some IT departments frown on connecting unauthorized equipment on their LAN as it could interfere with communications with other equipment on the LAN and pose possible security risks.
Having said that, your easiest solution would be to use the TL-R402M as a router and that means connecting the WAN side of it to the building LAN. If DHCP is not being used to assign IP addresses on the LAN, then you definitely need to talk to whoever is managing the LAN to find out what 10.xx.xx.xx address and sub-net setting you can use for the WAN side of the TL-R402M. The TL-R402M's DMZ setting could then be configured to use the PLC's fixed IP address. You would then be able to access the PLC from your computer using the 10.xx.xx.xx address for the WAN side of the TL-R402M. You should note that this will make the PLC accessible to anybody on the LAN.
Having said that, your easiest solution would be to use the TL-R402M as a router and that means connecting the WAN side of it to the building LAN. If DHCP is not being used to assign IP addresses on the LAN, then you definitely need to talk to whoever is managing the LAN to find out what 10.xx.xx.xx address and sub-net setting you can use for the WAN side of the TL-R402M. The TL-R402M's DMZ setting could then be configured to use the PLC's fixed IP address. You would then be able to access the PLC from your computer using the 10.xx.xx.xx address for the WAN side of the TL-R402M. You should note that this will make the PLC accessible to anybody on the LAN.