How do I quantitatively visualize this situation?
Two things will happen:

Firstly, everyone will effectively have had their real incomes rise by 10% (assuming this new energy costs nothing). They will then spend or save this income on other goods besides energy, increasing overall output (note, savings is used for investment as well).

Secondly, energy consumption will likely increase by a large amount now that it is nothing. People who were mindful about their energy consumption due to cost concerns will now not care. Therefore, people will be consuming more energy.