The R designator is a code that BW used to identify their unit to a specific OEM gear box. The R10-E you reference could be a Ford unit, probably early 50's. As Cletis states, it will not fit a Chevy. I have a Later Ford unit that is an R-11 1E. It is also completely different than a GM gear box. The most common OD trans is from 55-57 car/truck which has an R10 H designator.
58-65 car/truck has a rear mount pad and is an R10 K. I have one from a 64-65 Chevelle which is an R10 P. It has completely different internal gears and a fine spline output shaft.
Any of the GM units mentioned will bolt up to your bellhousing.
The full syncro Saganaw will work also, it can be identified by the 7 bolt side cover. Not sure what the BW designator code is.
You may get lucky. I have bought them for $50 to $100 and all they needed were bearings. Others were found to be total junk. You can't really tell until you tear them apart. If they look like they went down with the Titanic, then they are junk.
Fred

1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine