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This research proposes a novel algorithm, Neuro Differential Evolution (NDE), to optimize the topology and weights of neural networks. NDE makes a clear distinction between neural network topology optimization and weight optimization. A genetic algorithm (GA) is implemented to optimize the network topology as this is a discrete problem while differential evolution (DE) is applied to the network weights, which are continuous variables. The results presented in this paper demonstrate that this combined approach can successfully grow neural networks, from just a single neuron, that can produce feasible solutions when other methods fail. NDE outperforms the current state of the art neuroevolution algorithms on a range of increasingly complex reinforcement learning problems.