Actually, salt is the Old School way to help your fish cope with nitrite (it keeps it from destroying the gill tissue as much), so you did a good thing by adding it. Elevated salinity is going to be less stressful for your fish than an elevated nitrite level. You do, however, need to perform a partial water change to get your nitrite level down.
You should consider upgrading the tank if you are having problems with nitrite, as this level should be at zero. 8 silver tips tetras for a ten gallon is overstocked, so a 20 gallon would be a good thing to invest in. To avoid cycling it from scratch so you can move the fish over right away, run the old filter next to the new one in the new tank for several weeks, and seed your tank with a bacterial supplement.
I've used this method before when upgrading with great success. As for continuing to add aquarium salt, it need to be done in proportion with the amount of salt taken out each water change. If you take out 5 gallons, only add enough new salt to treat 5 gallons of new water.
As mentioned before me, Prime is another good alternative to temporarily detoxifying nitrites if you wish to stop adding salt.
You should not have Tetra's in a 10 gallon tank. And there should not be nitrites in the tank if your tank was properly cycled. You should have 0 ammonia 0 nitrites and under 40ppm NitAtes.
The salt won't help with Nitrites and Tetra's are sensitive to salt. I would add no more salt. Instead upgrade to a 20 gallon tank and begin cycling it.
In 6-8 weeks using pure ammonia it will be cycled and safe to add your Tetra's too. You would then have a stocked 20 gallon unless you wanted to add A dwarf gourami or Male Betta to that tank.
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