I have only seen examples where a difference-in-difference estimate is made with a regression of two variables and their interaction term, like the following equation:

Y=α+β1Treat+β2Post+β3(Treat ⋅ Post) +ϵ

β3 will be the difference-in-difference estimate for this regression and will give the p-values for the difference-in-difference estimate.

How do I write the regression equation with all six variables? Which constant will be the difference-in-difference estimate in that equation?

Resources or explanations on how to do this would be much appreciated. If you just know the answer to the first question I would appreciate that too.