|You can't do it with a formula, but you can do it with VBA.|
Right click the Sheet Tab for the sheet you are working with and choose View Code.
Paste this into the pane that opens.
Private Sub Worksheet_Change(ByVal Target As Range)
If Target.Address = "$A$1" Then Range("$A$2") = Now
Each time a change is made to A1, the Time and Date in A2 will update.