What is the EST light and what is wrong when it comes on and says check engine?

Here's what I was able to find on the Internet:

"ETS is Enhanced Traction System is used to stop wheel slip thru reducing engine output. And if the light is on it doesn't mean you will spend x amount of dollars to fix it! It just means that ETS has been disabled because you have a engine problem and the computer cannot reduce power to the wheels because the engine might stall so the computer disables the system! Now some cars come with a switch by the shifter that turns on and off the system because if you get stuck in the snow traction control will keep you stcuk.

Take my word on this for I am a GM Tech who is a Master ASE with L1 certified!

Generally when the ets off light is on (the only light on and not along with the check engine light) you may have a wheel speed sensor not responding. This can happen due to metallic dust on the sensor. Clean the 4 sensor locations at the local spray wash (each located on the hubs - look for the wires going to each)."
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From what's said above, I would have a mechanic remove each ABS sensor, using an external torx wrench, and clean it with a spritziled rag (don't use compressed air). Should be a very simple job. I would also make sure you have a tune-up (at least install fresh ACDelco platinum plugs and change the fuel filter). See if this solves the problem before doing anything else.