Can Future Energy needs be met sustainably?

Global energy use is increasing rapidly, driven by rising living standards in developing countries.  Although the percentage of primary energy provided by burning fossil fuels is falling slowly from its current value of some 80%, their contribution is rising in absolute terms and is expected to increase by around 25% by 2035.  This is bad news given the need to decarbonise (to reduce air pollution as well as to moderate climate change): is it inevitable?