How to open a stream for writing and then for reading?

Question

C++ / C#

Tried like this:

using (var stream = response.GetResponseStream())
{
    using (var sw = new StreamWriter(stream))
    {
        sw.Write("X");
    }
}

using(var stream = response.GetResponseStream())
{
    using(var sr = new StreamReader(stream))
    {
        responseString = sr.ReadToEnd();
    }
}

- on reading "The stream was unreadable"