Plants store solar energy as hydrocarbons. Further reformed into coal, oil, and gas, that's what we use today.
It's possible to synthesize hydrocarbons from seawater at a net efficiency likely around 50%. Hydrogen electrolysis is the primary energy cost at 60% energy delivered on input.
Run that from solar cells at 20% efficiency and you've got a net delivery of 10% of input solar as stored hydrocarbons. Mind that you're only going to extract about 30-40% of that as useful work or energy (electric generation is about 38% efficient in fuel conversion, cars around 10-20%, IC engines generally about 30%).
But the neat thing about hydrocarbons is that once you've got them, they can store for a long time. Hell, we've got proofs-of-concept showing 300-500 million year viability.
There are other options as well. Some are far more responsive (flywheel kinetic storage, pumped hydro), some far more efficient in energy input/output), others have varying degrees of suitability (CAES, thermal energy storage, liquid metal/molten salt batteries). I'm actually starting to see this as a potentially solved problem.