XNode.WriteTo Method

public abstract void WriteTo(
	XmlWriter writer
)

StringBuilder sb = new StringBuilder();
XmlWriterSettings xws = new XmlWriterSettings();
xws.OmitXmlDeclaration = true;
xws.Indent = true;

using (XmlWriter xw = XmlWriter.Create(sb, xws)) {
    xw.WriteStartElement("Root");
    XElement child1 = new XElement("Child",
        new XElement("GrandChild", "some content")
    );
    child1.WriteTo(xw);
    XElement child2 = new XElement("AnotherChild",
        new XElement("GrandChild", "different content")
    );
    child2.WriteTo(xw);
    xw.WriteEndElement();
}
Console.WriteLine(sb.ToString());

<Root>
  <Child>
    <GrandChild>some content</GrandChild>
  </Child>
  <AnotherChild>
    <GrandChild>different content</GrandChild>
  </AnotherChild>
</Root>