There are many types of fluorescent ballasts that can ignite SOX lamps, but do they operate them within specs of that particular lamp? Yes and no.
https://www.lighting-gallery.net/gallery/displayimage.php?pos=-143774https://www.lighting-gallery.net/gallery/displayimage.php?pos=-116715It appears that operating them just a few percent over specification will not harm them although I suspect their life gets shortened. You can however operate them by 30% less current and the lamps appear normal but definitely have less output, and may last as long as their rated life. This is where the WH2 comes in when hooked up to an 18w Sox or Sox-E. I would not attempt a WH2 on a 35w SOX, it's woefully inadequate.
These are the required currents for these lamps:
The 18W SOx is @ 0.35A
The SOX 35W & 55w lamps @ 0.6A.
The SOX 90W, 135W & 180W are @ 0.9A
Sox-E are different. Direct from the Philips catalog:
SOX-E 18, 0.36A @ 52 lamp volts
SOX-E 26, 0.45A @ 72 lamp volts
SOX-E 36, 0.36A @ 114 lamp volts
SOX-E 66, 0.63A @ 110 lamp volts
SOX-E 91, 0.63A @ 166 lamp volts
And SOX-E 131, 0.62A @ 238 lamp volts
Black ends are normal for LPS lamps. They disappear after many hours of operation.