You can accomplish this using WScript.Shell.SendKeys to trigger the goto line shortcut within TextPad (ctrl-G)
Dim wshshell
Set wshshell = CreateObject("WScript.Shell")
Call Shell("C:\Program Files\TextPad 5\TextPad.exe " & "C:\testfile.txt", vbNormalFocus)
Application.Wait (10)
wshshell.SendKeys "^g" 'ctrl-G
Application.Wait (10)
wshshell.SendKeys "15" 'desired line number
Application.Wait (10)
wshshell.SendKeys "{ENTER}" 'enter
You might have to mess with the Wait lines to add or remove delays between commands, but I tested this from within a VBA module in Excel and it worked.
I am aware that SendKeys that can be called directly from VBA, but when I tried to use that, it seems to be bound to the vba editor window.