Save and display value on TextBox from Session in ASP.Net

You need to use OnClick event to redirect from one page to another.

protected void Redirect(object sender, EventArgs e)
{
      Session["TextBox"] = this.txtTextBox.Text.Trim();
      Response.Redirect("~/Page.aspx");
}

And when you came back to same page check the content of Session.

protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        if (!this.IsPostBack)
        {
            if (Session["TextBox"] !=null)
            {
                this.txtTextBox.Text = Session["TextBox"].ToString();
            }
        }
    }
}