Our study addresses the issue of telework adoption by countries in the European Union and draws up a few feasible scenarios aimed at improving telework’s degree of adaptability in Romania. We employed the dataset from the 2020 Eurofound survey on Living, Working and COVID-19 (Round 2) in order to extract ten relevant determinants of teleworking on the basis of 24,123 valid answers provided by respondents aged 18 and over: the availability of work equipment; the degree of satisfaction with the experience of working from home; the risks related to potential contamination with SARS-CoV-2 virus; the employees’ openness to adhering to working-from-home patterns; the possibility of maintaining work–life balance objectives while teleworking; the level of satisfaction on the amount and the quality of work submitted, etc. Our methodology entailed the employment of SAS Enterprise Guide software to perform a cluster analysis resulting in a preliminary classification of the EU countries with respect to the degree that they have been able to adapt to telework. Further on, in order to refine this taxonomy, a multilayer perceptron neural network with ten input variables in the initial layer, six neurons in the intermediate layer, and three neurons in the final layer was successfully trained. The results of our research demonstrate the existence of significant disparities in terms of telework adaptability, such as: low to moderate levels of adaptability (detected in countries such as Greece, Croatia, Portugal, Spain, Lithuania, Latvia, Poland, Italy); fair levels of adaptability (encountered in France, Slovakia, the Czech Republic, Hungary, Slovenia, or Romania); and high levels of adaptability (exhibited by intensely digitalized economies such Denmark, Sweden, Finland, Germany, Ireland, the Netherlands, Belgium, etc.).