The function is

function ReadMWord(f: TFileStream): Word;
type
  TMotorolaWord = record
    case Byte of
      0: (Value: Word);
      1: (Byte1, Byte2: Byte);
  end;
var
  MW: TMotorolaWord;
begin
  f.read(MW.Byte2, SizeOf(Byte));
  f.read(MW.Byte1, SizeOf(Byte));
  Result := MW.Value;
end;

procedure GetJPGSize(const sFile: string; var wWidth, wHeight: Word);
const
  ValidSig: array[0..1] of Byte = ($FF, $D8);
  Parameterless = [$01, $D0, $D1, $D2, $D3, $D4, $D5, $D6, $D7];
var
  Sig: array[0..1] of byte;
  f: TFileStream;
  x: integer;
  Seg: byte;
  Dummy: array[0..15] of byte;
  Len: word;
  ReadLen: LongInt;
begin
  FillChar(Sig, SizeOf(Sig), #0);
  f := TFileStream.Create(sFile, fmOpenRead);
  try
    ReadLen := f.read(Sig[0], SizeOf(Sig));

    for x := Low(Sig) to High(Sig) do
      if Sig[x] <> ValidSig[x] then ReadLen := 0;

    if ReadLen > 0 then
    begin
      ReadLen := f.read(Seg, 1);
      while (Seg = $FF) and (ReadLen > 0) do
      begin
        ReadLen := f.read(Seg, 1);
        if Seg <> $FF then
        begin
          if (Seg = $C0) or (Seg = $C1) then
          begin
            ReadLen := f.read(Dummy[0], 3); { don't need these bytes }
            wHeight := ReadMWord(f);
            wWidth  := ReadMWord(f);
          end
          else
          begin
            if not (Seg in Parameterless) then
            begin
              Len := ReadMWord(f);
              f.Seek(Len - 2, 1);
              f.read(Seg, 1);
            end
            else
              Seg := $FF; { Fake it to keep looping. }
          end;
        end;
      end;
    end;
  finally
    f.Free;
  end;
end;

Example usage:

var width,height:word;
begin
  GetJPGSize(filename,width, height);
end;