Those particles of solar wind don't wander away from the Sun by the Brownian motion. They are ejected in Solar storms by electromagnetism. When many billion hydrogen atoms or rather ions conspire just in a right way, they can launch one of their own to the stars. The energy contribution of them many is needed, to accelerate just one.

Sometimes, a rock is ejected to the outer space by a volcano on Earth. That doesn't mean, the rocks here are that fast, 10 or more kilometers per second. But when a lot of rocks conspire in a just right way, one of them may be launched with such a speed from the Earth.

On the other hand, hydrogen molecules from Earth do wander away by the Brownian motion alone. 50 kilograms of them every second, according to Wikipedia, are fast enough to evaporate. And a few kilos of helium evaporates away from our planet every second as well.

Sun's gravity is too strong to permit a noticeable leak of this kind. Hydrogen atoms/ions on its surface are not that hot, that an observable fraction of them would gain the escape velocity. Paradoxically, on Earth they are!

That the Earth is loosing its mass I wrote something here.

I guess the Sun is gaining mass. Still.