Engines also had a serial number.
From an article I did on P40E
The P-40E in question was completed within the smallest batch of E models produced, towards the end of 1941. Many of the completed components were dated "08.41". This P-40E was supplied with the Curtiss construction number 16814 and the serial 41-13570. The order number was W-535 ac15802 and it cost the US government $39,628.00. Curtiss-Wright completed 79 machines within this block (construction numbers 16737-16815) and the serials 41-13521 to 41-13599 were assigned to them.
The Allison engine was a V-1710-39 that had the construction number 42-33729. The P-40E had been painted in Olive Drab 41 on the upper surfaces and Neutral Gray on the underside. It seems it had already been earmarked for the Soviet Union as it had been completed in nothing more than the serial number and stenciling. There was no sign of the American star having ever been applied.
http://lend-lease.airforce.ru/englis...very/index.htm
Sorry
Mark