You can't just invoice away all the profits from the Estonian company. That's basic tax evasion and risks getting picked up by the authorities. You'll trigger BEPS (Base Erosion and Profit Shifting) regulations if you artificially decrease the company's tax liability. If the amounts are small, it might slip through the cracks, though.
Not sure what else there is to say. You formed a company in a country that levies 20% tax at distribution, and now it's distribution time. Pay up and learn for the future.
Depending on how you've run your business, you might be able to claim certain costs and expenses against the Estonian company to reduce your tax bill. An Estonian accountant should be able to help you, if there are any transactions like that.
You have another headache, though. If the Estonian company hasn't had any directors/staff in Estonia, it might be tax resident in Switzerland (by having its effective management in Switzerland) in addition to Estonia, in which case you would need to invoke the Estonia””Switzerland double tax treaty to avoid double taxation ”” if you want to do things entirely by the book. Heavily dependent on the actual amounts involved.