You're going to jump through hoops to save it, plus you'd then have to worry about catching if anyone edited either of the fields so you could update it. I say just use the formula you already have on forms and reports when you want to display the value and not bother with the saving/updating.
I agree with Paul about not storing it! The part about recalculating it every time you need it could get tiresome. What I'd do would be to delete the CloseNum field from the table, then base my forms/reports on a query of the underlying tables, and in the query have a calculated field CloseNum. In a blank field in the Query Design Grid enter:
You didn't give us the error you were receiving, which makes remote diagnosis rather dicey, but in this situation, in the code module, the syntax would be:
Code:
Private Sub Form_AfterUpdate()
Me.CloseNum = Format(Me.DateClosed, "mmddyyyy") & Me.OrderID
End Sub