type
 TType = (mtMenuFaturamento, mtMenuRelatorios);
const
 StrType: array [TType] of string = ('MENU FATURAMENTO', 'MENU RELATÓRIOS');

uses System.Rtti;
...
 
procedure TForm1.BtnComRTTIClick(Sender: TObject);
var
  S: string;
  I: Integer;
begin
  I := Edit1.Value;
  S := TRttiEnumerationType.GetName(TType(I));
  ShowMessage('Tipo: ' + S + sLineBreak + 'Str : ' + StrType[TType(I)]);
end;

uses System.TypInfo
...
procedure TForm1.BtnSemRTTIClick(Sender: TObject);
var
  S: string;
  I: Integer;
begin
  I := Edit1.Value;
  S := GetEnumName(TypeInfo(TType), I);
  ShowMessage(
   'Tipo: ' + S + sLineBreak +
   'Str : ' + StrType[TType(GetEnumValue(TypeInfo(TType),S))]);
end;