I've been wondering if it's at all possible for a habitable tidally locked planet to not be a scorched wasteland on one side, an oasis in the twilight, and a frozen wasteland on the other, the planet instead having only one side of it be uninhabitable by being frozen while the sun-facing side is lush and green and full of life.
The planet is earth-like, from its mass to its atmospheric content and even its water and elemental content(materials like iron, silica, etc), in all respects except for it being tidally locked with the star of its solar system and having no axial tilt. The star of the system is also exactly like our sun. There is a moon that's the same as ours orbiting this planet at the same distance and orbital speed as ours as well, though its orbital path has a tilt of 23 degrees to prevent excessive eclipses.
At what distance from its star must this tidally locked planet be for the sun-facing side to be forested/entirely habitable while the dark side is frozen and uninhabitable?