Summary: Note that my impression is with the foam removed from behind the grills.
HD558 is a very good headphone that I would recommend to everyone to listen to. Easy to listen to, not offensive sounding or dark sounding. Good price.
No amp required.
Pros: Engaging, non fatiguing. Enjoyable sound signature. Detachable cable.
Summary: My chain: Lossless -> Foobar 2k -> HifimeDIY Sabre DAC -> E11
The HD558 are doing it for me right now. I was not blown away, but they really don't do anything wrong. The bass is not boomy but does bleed a tad, not ideal for classical but it's not hugely problematic.
The mids are nice.
Pros: Mostly neutral tonality, quality timber meets or exceeds expectations for the price, good presence across the spectrum, great all-rounders
Cons: Sennheiser veil, bass can bleed a little and doesn't go all the way down, mids not always as forward as I would like ideally