TSP (TriSodium Phosphate) is not the correct additive. It produces a precipitate, which is not a good thing for laundry and washing machines. TSP is typically used as an outdoor cleaner, such as for driveways/parking lots or prepping walls for painting, where a precipitate isn't objectionable.

The correct additive for laundry (or dishwashing) is STPP (Sodium TriPoly Phosphate), which does not produce a precipitate.

Slight difference in name, large difference in chemical properties.

I wouldn't want to use TSP on my laundry. It is great on the walls and ceilings, really cuts into the grease and grime. But for my delicate clothes no, I don't think so.

STPP is preferred over TSP, but only if you have hard water. There is little to no advantage using TSP/STPP if you already have soft water.

Be aware that STPP will decompose into TSP if you're not careful.

Several people here have used TSP but most recommend STPP instead.

What is your objective? Something as simple as Borax might serve your need or even a little better detergent.

Here is a link that might be useful: STPP FAQ