[Cormzy]

I have been trying to work out what the mechanism of this reaction is and how electrons are transferred.
I know that 2-methylprpane is formed but I don’t know why it reacts differently to a nucleophilic substitution reaction.

(CH3)3C-Cl + CH3CH2O-    (CH3)2C=CH2 + Cl-  + CH3CH2OH

[spirochete]

It's called E2 elimination. It happens because the halide is tertiary, so it can't do Sn2, and the reagent is a strong base, the Sn1/E1 paths are less likely, assuming that the base is not extremely dilute. If you tell me your textbook author and edition I could probably direct you to the pages to read.

[Cormzy]

Thank you very much,
The eliminiation content isn’t directly referred to in my textbook however the question showed the equation and expected some prior knowledge.
This advice is extremely helpful,
Many thanks,
Cormzy.

[spirochete]

Virtually all college level organic chemistry textbooks will have sections about the competition between substitution (Sn2/Sn1) and elimination (E2/E1), and also about the competition between carbocation pathways (Sn1/E1) and concerted bimolecular pathways (Sn2/E2).

[Babcock_Hall]

"2-methylprpane" is not the correct name of the product.  Perhaps you should name it as an exercise.