How to write uncertainties with the \pm symbol "10 ± 1 K" by using siunitx?

You want the separate-uncertainty switch, p.30 of the documentation.

\usepackage[separate-uncertainty=true]{siunitx}

sets this format for every number, or

\SI[separate-uncertainty=true]{whatever}

just for one.

I've just come across the same problem and this is how I solved it to my satisfaction:

in the preamble:

\usepackage[separate-uncertainty = true,multi-part-units=single]{siunitx}

in the text:

(\SI{284(10)}{\ampere})

Produces the following output: 284 ± 10 A

If multi-part-units=single option isn't given, the result will look like: ((284 ± 10) A) which, in my opinion, is less than optimal.

HTH