Obviously, the Avalon Eidolon is much too good a speaker to use with a "budget" amp. The better the amp, the better the Eidolon sound - - - however - - - there are a number of very good amps that may be purchased for under your $10,000 figure.
I sold a pair of Eidolons just over a year ago, and have regretted the sale ever since. I owned the Eidolons for almost 5 years and tried them with a number of "very good" amps.
You may recall that Keith Johnson (yes "that" Keith Johnson) had a hand in the design of the Eidolon speakers and is also the designer of the Spectral amplifiers. You might say that Eidolon speakers and Spectral amplifiers are made for each other - - and - - if you have ever heard them, you might say that they are a match made in Heaven.
The Spectral DMA-250 is the latest design from that firm and sells new for about $8500. This amp is unbelievably perfect for the Eidolon speakers. The problem with Spectral is that most of their amps require the use of a Spectral Pre Amp and dedicated MIT cables. This is not a problem sonically, because these component parts add to the wonder of the sound, but it certainly adds to the financial commitment.
Spectral, however, does offer amplifiers that work with other preamps and cabling. I've just not heard those amps. I own the DMA 250.
The Eidolon speakers are incredibly refined in their presentation and the Spectral amps allow the speakers to perform at their very best. If you have ever heard the term "holographic" applied to speakers, the Eidolon/Spectral combination will take the term to a new level. The sound will wrap around you and hug you.
I'm sure that the amps listed in the previous posts are excellent choices for the Eidolons because they are "good" amps. You just need to listen before you buy. There are also lots of other "great" amps that may be had at your price point.
I've actually heard the ARC VT-100 amp used very successfully with the Eidolons, as well as the VT-200. You actually may have just what you need already. You might find that you need more power, but you can evaluate the sound with the your 100 watts, and go from there. In my own situation, I preferred solid state on the Eidolons but tubes also sound wonderful.
I used Mark Levinson and Krell equipment for extended periods with the Eidolons and found the Spectral to be far superior. The Levinson and Krell amps just didn't match up well with the Eidolons. They lacked the refinement, speed and finesse that the Eidolons need to sound at their best.
I tried a Rowland amp (good), Classe (the Omega amp - great, but Spectral sounded better). I also tried a pair of Accuphase monoblocs that sounded wonderful but I couldn't afford them.
All in all, the Eidolons can provide astonishing sound within an incredible soundstage but the choice of a synergistic amplifier is critical to the overall sound of the speakers. It is hard to make the Eidolons sound bad but with a little work, you can make them sound fantastic.