Welcome to the Board!
You need a bit of VBA for that:
Private Sub Worksheet_Change(ByVal Target As Range)
Dim rng As Range
' Only look at single cell changes
If Target.Count > 1 Then Exit Sub
Set rng = Range("A2")
' Only look at that range
If Intersect(Target, rng) Is Nothing Then Exit Sub
' Add A2's value to B2
[B2] = [B2] + [A2]
End Sub
Right click the worksheet tab and select View Code. Paste the code into the module window that opens, then ALT+Q to exit back to Excel.
Type a number into A2 and see what happens.
Hope that helps,
Smitty