I don't have an erosion problem but the previous owner had a sandbox for the kids and when he decided to put in lawn they left most of the sand which causes the lawn to dry out real fast.

So about once a year I add kitty litter which is unfired clay. It really helps but it's not permanent.

For a more permanent solution you might try aerating and using a fired clay product like Turface (10 year life) which you can get a professional lawn product stores. But depending how deep your sand is, the only permanent solution is to remove and replace. The Turface in it self won't really help erosion but the plants will get better foothold.

It's kind of ironic for me too since my lot was bulldozed when the house was built to level it and there is no topsoil, just clay. Around my house is untouched native clay soil but it has a few inches of grit/sand on th surface. Around the outside perimeter of my house I see this sand fairly deep. I think this is what's left of the bulldozing of the lot. Perhaps that's what happened on your lot?

Here is the product specifically for sand based turf -

http://www.turface.com/turface-products/turf-conditioners/greens-grade

I use the MVP to help condition clay based turf.

Again, remember that only plants will stop erosion but you need an environment that will allow healthy root systems. If the root systems do not extend through the sand to underlying top soil/clay it still may not prevent erosion. Dig a test hole to see what you soil composition is at depth. Mosts grasses have a 8-10" root system at the most.