According to sources, 10K SR means solid 10K gold with SR as the manufacturer's mark.
Some might say that the SR means "silver". However, standard nomenclature or terminology would be .925 or sterling or some percentage, specifying the type of silver or percentage silver, not just silver.
“Karat” is a term that describes the purity level of gold. 10k gold is 41.6% gold, the lowest karat gold that can still be sold as “gold” in the US.
The most commonly found stamps on fine jewelry are hallmarks, also called purity or quality marks. These identify the relative proportion of precious metals -- gold, silver and platinum -- used in fine jewelry.
Initially established in 13th century England, hallmarks vary by country and time period. Contemporary U.S. jewelry uses the karat system, with 24 karats representing 24 out of 24 parts gold, or pure gold. A 14-karat gold item contains 14 out of 24 parts gold and is stamped 14k.
See AZCentral.com's How to Identify Jewelry Trademarks to know more.