How to both read and write a file in C#

You need a single stream, opened for both reading and writing.

FileStream fileStream = new FileStream(
      @"c:\words.txt", FileMode.OpenOrCreate, 
      FileAccess.ReadWrite, FileShare.None);

Don't forget the easy route:

    static void Main(string[] args)
    {
        var text = File.ReadAllText(@"C:\words.txt");
        File.WriteAllText(@"C:\words.txt", text + "DERP");
    }