There are a few general tactics that apply to your Magitech soldiers
- Capitalize on the Drow's anti-magic ability
- Use magic and magitech indirectly
- Train soldeirs to fight like a Drow
For the first point, MongoTheGeek has brought that up -- magic up something that is safe to be around that becomes dangerous when the magic is removed abruptly. A pit trap with a magical safety to allow people to walk on will basically trigger when an anti-magic drow walks on it. Pick your style of trap for this one.
The concept holds that in the absence of detecting magic, that you create a battlefield that is safe for the magical and a death trap for the anti-magic drow. Pit traps, land mines, falling anvils, snares ... pick your trap and magical safety and you have ideas.
If your magic has safety valves so this doesn't happen, then you either can't do it or you need spells/magitech that bypass these safety checks. Elfie wants big boom.
Since the elves have to be close to the magic so that it does not collapse on its own, they are the scouts and snipers. It will be all about finding the sweet spot of distance that lets the spell hold for them but fail once the drow disrupts it.
The second point works on the idea that so long you aren't trying to directly magic a drow, their inherent anti-magic cannot negate it. It tends to be the common loophole when dealing with kind of power. In this case, since the drow have an anti-magic aura of a non-specific size, the idea of blowing them up to destroy their stuff might not be a vaild one so a bit more creativity might be needed.
As an example, you use a spell to switch the places of a boulder-sized hunk of dirt and the air above the drow. The spell is over, but gravity is a harsh mistress and pulls the dirt down to the ground -- ideally directly on top of the hapless drow. And if you took the dirt from just below the ground, the drow could fall into the new hole, then get buried.
Magically cut down a tree and let it fall on people is another example. Lifting the ground out from under the drow might be an interesting idea if their aura is small enough to reach enough dirt.
The third point is to basically train a select group to fight in melee against a drow unaugmented by magitech or even just magic as a whole. Since the drow's weapons are going to be really good against the other elves, their combat style will reflect the idea that the first hit might be the only one needed to kill them or otherwise remove them from the fight.
Ranged weapons here won't be totally useless, but they will need to rely on being purely non-magical both in weapon and ammunition. This might be anathema to the elves' usual line of thiniking so it might not even be considered. Likewise their normal magitech is not useless in preparation, but they are required to be able to fight without it.