At first look, I would say no, it is not possible to stop this rather severe erosion by vegetation alone. Some sort of engineered solution will be needed. Is this a part of a stream system? Is there any chance of state grant money to assist in a project to repair this site? You might be surprised at what is available, depending on where you live, of course.

More likely than not, the only realistic way to mitigate this problem would be to regrade the slope-get it to a 2 to 1 or lesser slope. Then, vegetation will be needed to finalize the stabilization. This can and should consist of a combination of seeded, plant plugs, and maybe even live stakes, all to help hold things together.

I've been involved in several large-scale restorations of severely eroded ravines. I'm guessing that urbanization upstream from where this picture was taken is causing that waterway to become "flashier" than it originally was. IOWs, when a heavy rain event takes place, or even a moderate one, increased presence of roads, parking lots, rooftops, etc. on the upstream side is causing too much water to be immediately drained off into this channel. Such erosion is impossible to stop without taking serious measures.

If I'm wrong about the genesis of this problem, perhaps you will point out the discrepancies. But it sure does look like a small part of some large issues I've dealt with.

+oM

you could try something like Christmas ferns and boulders.
having said that, I agree with the above comments, you need to do some sort of grading.

Brush can be piled up in the gap area such that, over time, it collects more leaf litter, etc. Just be sure to not use branches from invasive species that might have seeds left on them! I've laid branches/brush into eroded gullies like this and achieved at least some success. I tended to think I was slowing the erosion down, not stopping it. And again, if this is what I think it is, areas upstream are being developed, with accompanying pavement and rooftops, and sending rain water down into this area in a hurry following rain events. Even agricultural lands can be "flashy" like that. In any case, that or something like that is the genesis of the problem, I suspect.

+oM