Updating A Column With A Count From Another Table?

My goal is to with one update statement, fill TABLE1.counter (currently empty) with the total count of TABLE2.e# (employee). Also, if TABLE1.e# isn't in TABLE2.e# then it sets it to "0" (TABLE1.e# 8 and 9 should have a counter of 0) This is for sqlplus.

e.g. TABLE2:

e#
--
1
2
3
4
5
5
6
7
7
1
2
3
4
5
UPDATE TABLE1
SET counter = (
SELECT COUNT(TABLE2.e#)
FROM TABLE2 INNER JOIN TABLE1 ON (TABLE2.e# = TABLE1.e#)
GROUP BY TABLE2.e#);

--^Doesn't work

so my TABLE1 should be:

e# counter
-----------
1 .. 2
2 .. 2
3 .. 2
4 .. 2
5 .. 3
6 .. 1
7 .. 2
8 .. 0
9 .. 0

(The .. is just spacing to show the table here)