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There's probably a more elegant way to do it but this should only update the matching rows:

update TableA A 
set email = (select email from TableB B where A.address_id = B.address_id)
where exists
      (select 1 from TableB B where A.address_id = B.address_id) ;

Another option is to use MERGE:

MERGE INTO TableA AS A
USING
  ( SELECT address_id, email
    FROM TableB
  ) AS B
  ON A.address_id = B.address_id
WHEN MATCHED THEN
  UPDATE SET email = B.email ;