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The code below does the job you describe. It is demonstrated in the attached workbook.
Sub DateTimeStamp()
' 11 Apr 2019
' modify constants as desired
Const Clm As Long = 2 ' identifies column B
Const StartRow As Long = 2
Dim R As Long
Dim Ref As String
With Sheets("Sheet1") ' change the name to match the tab name
R = Application.WorksheetFunction.Max(.Cells(.Rows.Count, Clm).End(xlUp).Row + 1, StartRow)
With .Cells(R, Clm)
.Value = Now()
.NumberFormat = "dd mmm yyyy" ' set the date format you desire
Ref = .Address
With .Offset(0, 1)
.Formula = "=" & Ref
.NumberFormat = "mm:hh:ss" ' set the time format you desire
End With
End With
End With
End Sub
Please take note of the comments in the code which tell you how you can modify the script.
Note that date and time is a single number in Excel, like 43876.63333. It seems too complicated to split this into two cells for display. The code just places a reference to the first cell into the second. You may like to consider using a single cell only and format the number as Date/Time with a format like this: "dd mmm yyyy hh:mm:ss"