Use file stream to read your data and then append the data to your rich text box
procedure TForm1.Button1Click(Sender: TObject);
var
FileStream: TFileStream;
data: TStringList;
begin
data := TStringList.Create;
RichEdit1.Clear;
data.LoadFromFile('D:\aa.txt');
RichEdit1.Lines.Append(data.Text);
data.LoadFromFile('D:\bb.txt');
RichEdit1.Lines.Append(data.Text);