Yes, it's doable w/o the carnet.
Check HERE.
The only question is if you can exit the country from another point that you entered the country (i.e. coming from Turkey and going to UAE). We had to exit from the same border post we entered to give back that "temporary import" document we issued, giving it back was obligatory.
Don't give up hope tho! Check it, maybe it's still doable from exiting another border point.
Good luck!
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