On how to remove the radiator,see this link for free factory service manual downloads:
http://www.t4x4pickup.com/dgroup/messages/2902.html
In North America the 22R & 22R-E s are used in the following:
22R
1981-82 Toyota Corona
1981-83 Celica
1981-87 Toyota pickup (up to 1990 on 2wd)
1984-87 Toyota 4-Runner
22R-E (22REC=California emissions=extra charcoal canister)
1983-85 Celica
1985-95 Toyota pickup
1985-95 Toyota 4-Runner
22RTE (Turbo EFI)
1985-87 Toyota pickup
1985-87 Toyota 4-Runner
so any of the above service manuals will have the same radiator.I recommend keep your old original brass/copper radiator and call of your local radiator shops found in your Yellow Pages and take it to the cheapest one to have recored.Afterwards spray a couple of coats of rust paint to reduce effects of fin corrosion from road salt.
If you insist on buying a new one this Washington state radiator dealer sell OEM rads to many reputable Toyota dealerships,their rads look identical to OEM with the exception of the cactus tree symbol.
http://www.performanceradiator.com
Sidney® ™
Repairs TV's,VCR's,home/car audio out of my apartment
E-mail:sidneybek(at)yahoo.com
Dartmouth,Nova Scotia
Canada