Sub NotEmptyDate()

    Const cSheet As String = "Sheet1"
    Const cCol1 As String = "A"
    Const cCol2 As String = "E"
    Const cFirst As Long = 2
    Const cLast As Long = 1000

    Dim i As Long

    With ThisWorkbook.Worksheets(cSheet)
        For i = cFirst To cLast
            If Not IsEmpty(.Range(cCol1 & i)) Then
                .Range(cCol2 & i) = Date
            End If
        Next
    End With

End Sub