Why the engin light and trac off light are on on my toyota corolla 2010?

Other answer:

In all modern Toyota/Lexus vehicles VSC and TRAC, if equipped, are disabled when the ECU displays the CEL. When you have the engine light fixed the TRAC will work again. It is not an ABS sensor or similar: that will light the ABS warning. Similarly, wheel pressure sensors light the tire pressure warning light. If something is actually wrong with the TRAC system, the TRAC light will flash rather than staying lit.

I no longer recommend people go to Auto Zone or other parts stores to have the codes read. Far too many people are sold parts they don't need, especially O2 sensors. Have a mechanic take care of it from beginning to end.

don r:
Scan it and see. You can turn Trac on or off with a button on the lower left of the dash. The engine light means there is a malfunction, but to see what that means a code scanner needs to be used. Car part stores will scan for free. Do not abbreviate the code when you get it, and look up the meaning of the code before trying to guess. When the road becomes slippery, the trac off will activate; a rain downpour can be such a situation. By the way, do you have a low tire? Look at them. Low tires can be slippery. By now the tire pressure system monitors might have weak or dying batteries, possibly making warnings unreliable or false. Those monitors are quite expensive to replace. Some tire shops, such as Big O have a computer that can examine each one on your car.
Bad wheel speed sensor. You need an ABS scan tool to read the codes and find out which of the 4 sensors it is.
Go to Auto Zone and find out.