I had a Sennheiser RS 170 (slightly lower than HD 518) wireless. People said an amp makes no difference.
I tried without an amp and it sucked bad.
I tried a Fiio E11 and the sound improved, but it still wasn't enjoyable.
I tried my Asus STX and the headphones were finally worth listening to. Still there was a veil and it wasn't perfect, but the sound was much better.
I tried a Lehmann BCL at the Senn showroom, sounded awesome, didn't buy it though.
Then I got a Bravo Ocean which took sound to the next level compared to Asus STX.
And Project Ember was a step up from even the Bravo, now comparable to the BCL amp.
So, in my experience, with even a simple headphone like Senn wireless RS series, the amp makes a huge difference. And these are 32 ohm headphones.
I haven't used HD 558 but I have used HD 518 and HD 598 and yes the amp does play an important role.
Thank You
Aakshey