Text similarity using RNN
Doc2Vec, Mikolov's paper will solve your problem. Here is the paper. You can find a gensim implementationhere. While using RNN, using GLOVE or Googl Word2Vec will be always useful even if your sequences are of the same length. To solve the variable sequence problem you can pad the sentences and use bucketing or just pad to one uniform length, truncating longer sentences and padding shorter sentences.