In a SQL database, how do I delete from table A without deleting a matching row in table B?

When you delete rows from table A, no deletions will occur in table B unless you have specifically created, in table B, a foreign key with the ON DELETE CASCADE property, that references the primary key of A.

Assuming you haven't done that, the following query will delete matched rows from table A:

delete
  from tableA
 where exists
       ( select 1 
           from tableB
          where email = tableA.email )

This should work in all databases.

Some databases have their own specific DELETE syntax. In Microsoft SQL Server, for example, you could also say:

delete tableA
  from tableA
inner 
  join tableB 
    on tableA.email = tableB.email

This accomplishes the same result; rows are deleted from table A only.