You can try it in the following way. First fit two models: model 1 is y = beta0 + beta1*x1 + beta2*x2, model 2 is y = beta0 + beta1 *(x1+x2). Compute the Residual Sum of Squares for model 1 and for model 2, respectively, denoted by RSS1 and RSS2. Then calculate the statistics T = (RSS2-RSS1)/(RSS1/(n-3)) that has a F-distribution with parameters (1, n-3), where n is the number of observations. So you can apply it to test your problem. For more general problem with more than two variables, the above statistics can be used as well just with a need to modify the degrees of freedom of F distribution.