You need VBA for this. A formula cannot do what you want.
Right-click the sheet tab.
Select 'View Code' from the context menu.
Copy the following code into the worksheet module:
Private Sub Worksheet_Change(ByVal Target As Range)
Application.EnableEvents = False
' Change C1 to the cell in which you want the time stamp
Range("C1").Value = Now
Application.EnableEvents = True
Switch back to Excel.
Save the workbook as a macro-enabled workbook (.xlsm).
Make sure that you allow macros when you open the workbook.