Welcome to the forum!

First, you need to use the "code" tags around your code. Edit your post and you can fix it.

Second, here is a solution to your problem. Since the Target variable is for only a single range, your And is not working. This solution checks the C8 and C16 cells directly without using Target.
Private Sub Worksheet_Change(ByVal Target As Range)
If (Me.Cells(16, 3).Value <> "" And Me.Cells(8, 3).Value <> "") Then
    Range("E:E").EntireColumn.Hidden = True
Else
    Range("E:E").EntireColumn.Hidden = False

End If

End Sub