Yes, the device-drivers can be downloaded from the Internet, to one computer, and then burned onto a CD-writable, or written to a USB memory-stick, and then the files can be physically moved to the other computer.
But, "which" device-drivers is completely dependent on which computer that you have. Some motherboards have "integrated" network-adapters and "integrated" USB-ports.
Easiest solution is to take an add-in PCI network-adapter card, and install it, and connect the Ethernet cable to its socket.
Hopefully, Windows will recognize that card, and automatically load the correct device-drivers from the C: drive, i.e., without Internet access.
Or, if you buy an add-in card, it may come with a CD-ROM that contains the device-driver.
Once the device-drivers have been installed, you will have Internet connectivity. Access: http://WindowsUpdate.Microsoft.com
and click "Custom" scan, and then click "Optional Hardware".
Windows Update should find the device-drivers for your motherboard, and install them. Then, you can remove the add-in card, and connect the Ethernet cable to the "on-mother-board" network socket.