Good news guys: I did some random Googling, and I found the solution; it mostly involves installing python3-smbc, adding a dummy account and a new PPD.

I'll write the solution in a minute as soon as I organise my thoughts.

My latest challenge is to do the same thing on command line so my remaster tool Cubic can do this for all accounts created on the Mint and Trisquel computers in my household.

Somebody help me!

EDIT: Most specifically, I would sum up the second-last paragraph to, how do I add external ppd files to the Mint printer database using the terminal?

OK, I solved the issue after some random Googling and this is what I did:

1. Install python3-smbc. For printers being shared through the SMB protocol, you would have to install python3-smbc or nothing in the Printers configuration will work.
   
2. Create an account on your Mint that matches one in the Windows 10 computer sharing the printer. Use it when you're asked to login and put it in login/password textboxes in Set Authentications menu. Don't forget to check the Set Authentications option radio button as well. Click Forward and go to the Devices Selection Menu.
   
3. Go to a site like OpenPrinting and download the appropriate PPD file that matches your printer and the device type. My printer is HL-2140 and I chose the hl1250 PPD. Back of the Printers configuration: this is where you pick the PPD file that you downloaded. Click on the choose PPD option and pick the PPD file.

You should now be able to print; print a test page to see if I'm right. I know I was when using that formula in my Linux Mint box and my Trisquel GNU/Linux box.

That's what I did and it seems to work, no joke. I'm no computer expert as I just used everything that I read randomly, so I don't what your situation was if you couldn't get yours to work. Just RRTFM, I guess, or "randomly read the f**king manual."