What it consists of:

The AS (Artificial Sun) would consist of 2 main parts, the fusion reactor that creates the energy required to fuel the AS and an engine system that could bring the fusion reactor into space.

Fusion reactors, are a topic being continuously explored on and expanded in today's world, and only requires the isotopes of hydrogen to create the energy required to power the AS. Hydrogen, being in abundance on TRAPPIST-1 e, means that getting the fuel to power this Artificial Sun will not be an issue.

The Engine System, which will be used to bring the AS off the exoplanet and potentially keep it in orbit  above the Luxternal Region would be the same technology currently being used in rockets and the ISS.

How it solves (half of) the tidal locking problem:

With the Artificial Sun Fusion Reactor running above the Noxturnal Region, it will provide light and warmth to an otherwise inhabitable dark and cold region. This essentially frees up the previously unusable region of the planet and makes more space for cities, factories, farms, etc. to be built on TRAPPIST-1 e.

How the Artificial Sun creates more usable energy:

Producing a large amount of light energy, solar panels built at the closest part of the planet to the AS would be able to become an efficient energy farm, providing more energy for civilization.