If you're updating, then why not put the UPDATE in the trigger? Something like this:

ALTER TRIGGER [dbo].[tr_datediff] ON [dbo][JOURNAL]  FOR INSERT,UPDATE
AS
Update mytable
set mycol = DATEDIFF(d,start_date,end_date)[diff]
FROM inserted

If the column to be updated is in the table, then join back to the Journal table with inserted to find the correct row.