Try this,
<asp:TextBox ID="Txt_First" runat="server"></asp:TextBox>
<asp:TextBox ID="Txt_Second" runat="server" Width="280px" TextMode="MultiLine"></asp:TextBox>
<asp:Button ID="Button5" runat="server" onclick="Button5_Click" Text="Button" />
protected void Button5_Click(object sender, EventArgs e)
{
string text = (Txt_Second.Text) + "\r\n" + Txt_First.Text;
Txt_First.Text = "";
Txt_Second.Text = text;
}