Using a combination of the Worksheet_Change, Worksheet_SelectionChange and a global variable (in a module), this may work for you.
The following code goes into the worksheet code module for the sheet with your tasks/dates (right-click tab, select View Code, paste this code into the VB editor)
This line of code sets a global variable, and goes in a module. In the VB Editor, click Insert > Module, then paste this line. It basically captures the cell value of any cell you click on while on the sheet with the 'SelectionChange' event code. This is so it can compare the previous value with the new value. (If the cell was "Test Task 1", and you re-type "Test Task 1", you probably don't want the date to change, hence this check. If it was "Test Task 1" and now it's "Test Task 2", a new date will appear in column B.)
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