no, what i meant by that is that the e10k is a DAC plus amplifier in one unit not just a dac. basically soundcards are also dac+amplifiers as well. you can read that statement as "either a soundcard or something like the e10k would fix your issue most likely". i wanted to make sure i said dac PLUS amp because i did not want you going out and accidentally buying only a DAC (although the e10k you were looking at is fine since its a dac+amp).
i purposefully said it as dac+amp to avoid any confusion with external dac only units.
just for reference, an external DAC-only (an example of this would be the schiit modi) just converts the signal from digital to analog and does not output enough power to drive headphones (but will work with self powered speakers). DAC only units get paired up with amplifiers (the schiit magni often gets paired with the modi for instance. basically a dac+amp unit just combines both boxes into one.