Determine the type of filter from the transfer function i got that system $x_n \to x_n-x_{n-1}$, so $h_n=[.....,0,1,-1,0,...]$, with $h_0=1$ and $h_1=-1$, so the transfer function given by:

$$\sum_{i=-\infty}^{\infty} h_ne^{-jwn} = h_0e^{-jw(0)}+h_1e^{-jw(1)}=1-e^{-jw}$$. How to knwo the type of filter, if it is HPF, LPF, etc.

I appreciate your help.
That is an FIR filter transfer function.

Plot the frequency response to determine if it is HP, BP, LP.  

(Hint: compare the magnitude at w=0 and w=pi to get a quick idea)

This seems like a homework problem, so I don't think it is appropriate to supply a complete answer.