How does LEFT JOIN with WHERE clause works?
The query optimizer will decide and it is pretty smart.  

SELECT * FROM tableA 
LEFT JOIN tableB 
  ON tableB.id = tableA.id
WHERE tableA.name = 'e'  


There are many cases where doing the join first is more efficient.  If name is indexed and 'e' is somewhat unique then do that first is more efficient.

This is different  

SELECT * FROM tableA 
LEFT JOIN tableB 
  ON tableB.id = tableA.id
WHERE tableB.school = 'EE'   


That changes the left join into an inner join but since there is a match in your data you would get the same results.