So Box E on Releve 1 is actually the amount of tax deduction for Quebec and box 22 on T4 is the amount withheld for federal income taxes. That is why they are different.
You need to remember that province of employment is Quebec and not BC.
The rule of residency for the tax purposes is that between BC and Quebec, in whichever province the taxpayer spent his/her last day of the year (December 31), must file taxes with that province.