We could achieve a stable population, but we're still growing our energy use - and will be for some time, as there's something like 2 billion people who also want to have western living standards (like hot water and washing machines).
This is not entirely true - in the developed world, energy use per capita has been stable for many decades now, currently economic growth has been decoupled from energy usage, breaking the assumptions of 70s "The Limits to Growth" argument. There's no exponential growth trend; yes, the total energy usage will grow while the population is (still) growing; yes, the energy usage per capita in developing countries will eventually increase to match developed countries, but that's it, there's expected growth but it is limited.
Our continuing progress and well being does not rely on unbounded growth of energy use until it inevitably hits a ceiling; we can expect total energy demand to stabilize at some level (though higher than the current one), and there's no reason why we couldn't meet that energy demand with sustainable means. There's no revolution needed to lift the ceiling - the ceiling we need is within sight, and we can reach it with straightforward application of current technology, e.g. increased adoption and economy-of-scale cost reduction of currently available solar and battery technology among others.
