<?xml version="1.0" encoding="utf-8"?>
<List>
  <Email_Entry></Email_Entry>
  <Email_Entry EmailID="qw@gmail.com" />
  <Email_Entry EmailID="qw@gmail.com" />
  <Email_Entry EmailID="qw@gmail.com" />
  <Email_Entry EmailID="qw@gmail.com" />
  <Email_Entry EmailID="shssh@gmail.com" />
</List>

string EmailID = txtEmailSubscribe.Text;
        string FILE_PATH = Server.MapPath("~/Logs/SubscribedEmails.xml");

        XDocument Emailxml = XDocument.Load(FILE_PATH);
        var EmailExist = Emailxml.Descendants("Email_Entry")
            .Any(x => (string)x.Element("EmailID") == txtEmailSubscribe.Text);
        if (EmailExist)
        {
            lblEmail.Text = "EmailID already exist";
        }
        else
        {
            Emailxml.Root.Add(new XElement("Email_Entry",
                       new XAttribute("EmailID", EmailID)
                   ));
            Emailxml.Save(FILE_PATH);
            lblEmail.Text = "Subscribed Successfully";
        }
    }