How to substract/add 2 signals which have different phase?

Currently, I want to finding the different of 2 signals in Timedomain. The data is time and amplitude.

I have tried xcorr function with fft, but I cannot find how to do the phase shift with xcorr to make 2 signals in phase and then I can substract them.

It is hard to represent the signal by cosine function, so I really want to find the solution directly by data.

The attachment is my 2 data sets.

Here is how I do as suggestion from other thread:

[c,lags]=xcorr(Y1,Y2);
[~,iLag]=max(c(find(lags==0):end));
s3=circshift(Y2,[0 iLag]);

[nanren888]

What do you mean by subtract/add?

z = x+y;

Can you explain what you actually want?

Your use of xcorr is as if you want to align them in some way.

is Y1 X1?

Is Y2 X2?

[Nguyen Trung Kien]

Yes, I mean I want to find the signal which is difference between 2 signals:

z = y - x;

But I have only echo data as in attachment in time domain, I cannot represent signal by cosine function.