Trouble understanding an article about MFCC
So the output of the Discrete Cosine Transform gives a 13-vector. To this, they append the log mean energy. That gives a 14-vector.

They then subtract from this the previous 14-vector to yield another 14-vector, which they concatenate with the existing 14-vector.

That gives a 28-vector.

I suspect the log mean energy is just:
$$
{\tt LME} = \log\left(\frac{1}{N} \sum_{N} x_n^2 \right)
$$
where $N$ is the length of the frame used.