Which SS amplifier has similar sound as the LTA amplifiers?....

Interested in buying an amp that has detail and transparency and at same time some qualities and characteristics of tube amplifiers. I do not want to deal with tubes anymore (heat and maintenance)
Dan—LTA amps are not like other tube amps. Almost no heat and extremely long tube life. Plus—incredible sound. Really truly the best of both worlds. 
yes I’m aware that LTA amplifiers are different than traditional tube amplifiers but quite expensive for a HS teacher nearing retirement, I should have mentioned around $3000.

There is no SS amp in your price range that can match an LTA offering. My CODA #16 comes closest but at 13K. My ZOTL40 is a care free, maintenance free amp. The tubes in it will probably outlast me. I would check out the used market.
There’s a used Valvet E2 available here for $1850.  It’s Class A, but it’s small so isn’t as much of a space heater as the larger, more powerful beasts out there.  Read the reviews if you haven’t.  Best of luck.