Invisibility is broken - that is not a statement that is a fact, accepted by wide assortment of people in the community. There would be ways to tone it done but at the moment, for the meager amount of Warp Charges required to cast it, its Waaaaheheheheheeey over the top.
Heh, from your post - be glad you didn't face the invisible Flying Daemon Circus. Or the summoning ring - pretty much exclusive to daemon armies (though others can do this to, GK for eg.) that use tons of cheap pink horrors to summon more and more and more deamons - oh... and they have more than 19 dices for their power pool :3
Anyway - yeah, some armies which don't have psykers, or "propah" psykers (looking at you weird boyz
) usually have other stuff to mitigate - for example Necrons - being almost immortal with their extra save in reanimation, etc.
The problem with your batle is that the current Codex CRAFTWORLDS Eldar, is like the previous codex on steroids. And the previous one was already pretty darn good. They are faster, hit harder, and have something strong to deliver in every single game phase. Whereas we have no psychic phase, and our close combat is like beating a tank with a stick... and that's being said IF the tank doesn't squish you in the process.
As a Tau due to all this you need your shooting phase to be twice as effective to make up for those two phases which we either lack completely, or are utterly bad in it. Sadly the things Eldar can cast on their units negates this a lot... and thats just by using their own codex Powers, not even tossing into the calculation things like Invisibility and such.
Eldar are a tough match up over all. Even without their psychic phase. The best advice would be to try negotiate with your friend some terms - like sure go for "Elf magic roller" but lets say, don't use Invisibility which (obviously broken) can single highhandedly ruin the game for you.
That and then just wait for our new dex, which should be dropping (hopefully) soon, lets hope no later than October.... and hope that we get our proper power creep level up as well.
Sorri for not having any better tactics or strategies for you, but psychic phase can do either awesomely or do absolutely nothing... in case of Eldar the first one is the case more often than not.