How to SUPPPPRESS light from a star that is ten billion times brighter than its habitable exoplanet

Searching for Earth 2.0 has been an obsession of almost all exoplanet hunters since the discipline's dawn a few decades ago. Since then, they've had plenty of technological breakthroughs help them in their quest, but so far, none of them have been capable of providing the clear-cut image needed to prove the existence of an exo-Earth.