The original code has some fixed assumptions about the data

1) The file names will always be in column "E"
2) The data to be written will always be in column "J" ( i.e. col 10)
3) The file name is on the same row as the data to be written.

If you are planning on keeping those basic assuptions then this should work. 

Sub SaveSelectedRows()
    Dim i As Long, LastDataRow As Long, StartRowNum As Long, EndRowNum As Long
    Dim MyFile As String
    Dim fnum, s
    Dim UserRange As Range

    'On Error GoTo Canceled
    Set UserRange = Application.InputBox(Prompt:="Please Select Range", Title:="Range Select", Type:=8)

    With UserRange
        StartRowNum = .Cells(1, 1).Row
        EndRowNum = .Cells(.Rows.Count).Row
    End With

    LastDataRow = ActiveSheet.Range("E" & Rows.Count).End(xlUp).Row

    If EndRowNum < LastDataRow Then
        LastDataRow = EndRowNum
    End If

    For i = StartRowNum To LastDataRow

        '--  Text Files Names : Column E
        MyFile = "C:\Users\DJ-PC\Desktop\Text\" & ActiveSheet.Range("E" & i).Value & ".txt"

        '-- Save Text in Column 10 (Column J) Cells
        s = NewLn(Cells(i, 10).Text) & vbNewLine

        fnum = FreeFile
        Open MyFile For Output As fnum
        Print #fnum, s
        Close fnum
    Next i
End Sub
If you want to change those restrictions, for example, specifying another column for filenames, then you'll need to explain more about how you want to change things.