No, you shouldn't need any addtional parts. If the 18"s had a 48 mm offset compared to the 45 mm offset on the 20s, you won't notice a difference. Or do the 20s have a 35 mm? I can't tell from your post. Even at a 35mm, the 20s will sit 13 mm closer to the center of the car, but, if they are wider than the 18s, the outside face of the wheel will be about the same.

Bottom line (that was a confusing answer ) is that you should be able to just bolt the 20s on with no mods.