To find the maximum value in a string of cells (or a row in this case) use the following:
=MAX([row])
As an example, the maximum value in row 1 will be returned using the below equation:
=MAX(1:1)
This can also be used to search for maximum values in columns such as:
=MAX(A:A)
Cheers.
::EDIT FOR RESPONSE::
Thank you for adding an example. To achieve what you are looking for, I would recommend using the following formula if your data falls in column A, and then copy it downward as far as you need:
=IF(MAX($A:$A)=A1,A1,"")
Do note that if you have more than 1 row that contains the same maximum value for your data series, the maximum value will appear in your adjacent target cells for each instance that this happens.