Is there a way I can make this image look better when white on a dark background thanks

looks blown out and unclear when inverted

Most images will, and good reasons for inversion are extremely rare. (One good reason is to produce an effect in which the image is 'blown out and unclear'.) What is your objective? If it is to get a black background, that can work, but not by inverting the whole thing; the dog's shadows and highlights have to stay logical (as opposed to the illogic of their reversal by inversion). A quick and dirty mask done in Photoshop demonstrates that:

Of course a truly marketable result would take more time.

Is there a reason that you want to invert the graphic? It seems like it would be better if removed the background and made it black.

If it's a flattened raster graphic, you might want to use Photoshop instead.