The scanner uses a separate scanner driver (Country specific web sites, try the direct link Brother_ScannerDrivers_1_0_0.dmg.
Found it by search for MFC-7820N and filtering for 10.10.
Looking in the install package contained within there's a Brother Scanner.app. Shows a date of October 10, 2014.
The MFC-7820N is listed in the com.brother.DeviceDB.plist for the app.
It also contains a TWAIN driver.
If that doesn't work by itself see TWAIN Scanners in OS X Maverick (and Yosemite).
I don't have a Brother scanner to try it. Apple supports a lot of printer/scanner vendors directly (Cannon, Epson, FujiXerox, Gestetner, HP, Infoprint, Infotec, Lanier, Lexmark, NRG, Ricoh, Samsung and Savin), although I'm sure with vendor help. Notice Brother is missing from the list.