Why does Solas give the orb to Corypheus?
Because he is too weak to unlock it.
If you unlock the orb, what do you get?
The Anchor.
What does the Anchor allow its bearer to do?
Move through Veil, as a needle pulls thread, and enter the Fade physically.
How else can the Fade be physically entered?
By re-tuning an eluvian to the Fade.
Who can re-tune an eluvian to physically enter the Fade?
Flemeth (housing the soul of Mythal) and Keiran (housing the soul of Urthemiel).
What significant place can be reached by physically entering the Fade?
The Black City.
Theory:
Solas needs the soul/power of Flemeth for the same reason he wanted Cory to unlock the Anchor for him: to physically enter the Fade and reach the Black City.
What is in the Black City?
Something to do with the Blight. According to the notes of Avernus (a gray warden mage):
In my dreams, I see the Black City, and I am drawn towards it. There is something there, an answer to what this taint is, this taint that we share with the darkspawn...
Wait, this makes no sense. If Mythal can re-tune an eluvian, why can't Fen'Harel?
Beats me. Maybe he's not a 'god' in the same way she is. Stop asking so many questions and go to sleep!