Notice how the pic, at least, of the E2TE-CHA shows a Carter YFA and the E1TE-CHA pic shows a 2150? That's the issue here - a seemingly minor change in the part number can make dramatic differences in the part.
While it is possible that the E2TE-CHA really did come on some 1982 truck, it isn't likely it came on an '81 with the E2.
Anyway, I can't tell you want a carb w/a E2TE-CHA tag fits.
Gary, AKA "Gary fellow":
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Dad's: '81 F150 Ranger XLT 4x4: Down for restomod: Full-roller "stroked 351M" w/Trick Flow heads & intake, EEC-V SEFI/E4OD/3.50 gears w/Kevlar clutches
Blue: 2015 F150 Platinum 4x4 SuperCrew wearing Blue Jeans & sporting a 3.5L EB & Max Tow
Big Blue: 1985 F250HD 4x4: 460/ZF5/3.55's, D60 w/Ox locker & 10.25 Sterling/Trutrac, Blue Top & Borgeson, & EEC-V MAF/SEFI